Lineability and K-linear discontinuous functions

It is well known that there are Q-linear discontinuous functions from R to R. Moreover, such functions have dense graph in the real plane. In this paper, we study the existence of linear spaces contained in the family of linear discontinuous functions in the generalized context of topological vector...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Linear algebra and its applications Jg. 645; S. 52 - 67
Hauptverfasser:	Fernández-Sánchez, J., Rodríguez-Vidanes, D.L., Seoane-Sepúlveda, J.B., Trutschnig, W.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Amsterdam Elsevier Inc 15.07.2022 American Elsevier Company, Inc
Schlagworte:	Absolute value Discontinuous function Everywhere surjective Field Lineability Linear algebra Linear function Normed space Strongly everywhere surjective Topological vector space Vector spaces Lineability 12J99 Linear function Strongly everywhere surjective 46S10 46B87 Normed space 15A03 Field Everywhere surjective Topological vector space Discontinuous function Absolute value
ISSN:	0024-3795, 1873-1856
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Abstract	It is well known that there are Q-linear discontinuous functions from R to R. Moreover, such functions have dense graph in the real plane. In this paper, we study the existence of linear spaces contained in the family of linear discontinuous functions in the generalized context of topological vector spaces and fields endowed with an absolute value. Furthermore, in the case of fields endowed with an absolute value, we study the algebraic genericity of the families of (1) linear discontinuous functions that are not everywhere surjective and (2) linear discontinuous functions that are strongly everywhere surjective. This extends a number of previous results of lineability theory. Generalizations of classical results of Q-linear discontinuous functions are also analyzed.
AbstractList	It is well known that there are Q-linear discontinuous functions from R to R. Moreover, such functions have dense graph in the real plane. In this paper, we study the existence of linear spaces contained in the family of linear discontinuous functions in the generalized context of topological vector spaces and fields endowed with an absolute value. Furthermore, in the case of fields endowed with an absolute value, we study the algebraic genericity of the families of (1) linear discontinuous functions that are not everywhere surjective and (2) linear discontinuous functions that are strongly everywhere surjective. This extends a number of previous results of lineability theory. Generalizations of classical results of Q-linear discontinuous functions are also analyzed. It is well known that there are R to R. Moreover, such functions have dense graph in the real plane. In this paper, we study the existence of linear spaces contained in the family of linear discontinuous functions in the generalized context of topological vector spaces and fields endowed with an absolute value. Furthermore, in the case of fields endowed with an absolute value, we study the algebraic genericity of the families of (1) linear discontinuous functions that are not everywhere surjective and (2) linear discontinuous functions that are strongly everywhere surjective. This extends a number of previous results of lineability theory.
Author	Rodríguez-Vidanes, D.L. Seoane-Sepúlveda, J.B. Trutschnig, W. Fernández-Sánchez, J.
Author_xml	– sequence: 1 givenname: J. surname: Fernández-Sánchez fullname: Fernández-Sánchez, J. email: juanfernandez@ual.es organization: Grupo de investigación de Análisis Matemático, Universidad de Almería, Carretera de Sacramento s/n, 04120 Almería, Spain – sequence: 2 givenname: D.L. orcidid: 0000-0002-1016-096X surname: Rodríguez-Vidanes fullname: Rodríguez-Vidanes, D.L. email: dl.rodriguez.vidanes@ucm.es organization: Instituto de Matemática Interdisciplinar (IMI), Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Plaza de Ciencias 3, Universidad Complutense de Madrid, 28040 Madrid, Spain – sequence: 3 givenname: J.B. surname: Seoane-Sepúlveda fullname: Seoane-Sepúlveda, J.B. email: jseoane@ucm.es organization: Instituto de Matemática Interdisciplinar (IMI), Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Plaza de Ciencias 3, Universidad Complutense de Madrid, 28040 Madrid, Spain – sequence: 4 givenname: W. surname: Trutschnig fullname: Trutschnig, W. email: wolfgang@trutschnig.net organization: Department for Mathematics, University Salzburg, Hellbrunnerstrasse 34, 5020 Salzburg, Austria
BookMark	eNp9kEFLwzAUx4NMcJt-AG8Fz60vSdMseJKhUxx40XNIkxRSajKTVNi3t2WePOz04PH_vcf_t0ILH7xF6BZDhQE39301KFURIKQCWgHwC7TEG05LvGHNAi0BSF1SLtgVWqXUA0DNgSwR7J23qnWDy8dCeVO8lcO8iYVxSQefnR_DmIpu9Dq74NM1uuzUkOzN31yjz-enj-1LuX_fvW4f96UmjOVStBy62gjWCMo1Z1oxRYSgBATBVOG2bZTFFJOGCSUY1BuoNasNgOHCEEHX6O509xDD92hTln0Yo59eSsKhpsAamFP4lNIxpBRtJw_Rfal4lBjkLEb2chIjZzESqJzETAz_x2iX1VwuR-WGs-TDibRT8R9no0zaWa-tcdHqLE1wZ-hfvqx82w
CitedBy_id	crossref_primary_10_1016_j_jmaa_2025_129234 crossref_primary_10_1007_s00025_023_01933_3 crossref_primary_10_1007_s00025_023_02121_z crossref_primary_10_1007_s13398_024_01561_8
Cites_doi	10.4064/sm-5-1-69-98 10.1016/j.jmaa.2006.03.025 10.1090/S0002-9939-2010-10420-3 10.1016/j.laa.2006.02.041 10.7146/math.scand.a-15057 10.1016/j.jmaa.2004.01.036 10.1090/S0273-0979-2013-01421-6 10.1515/math-2017-0042 10.1090/S0002-9939-04-07533-1 10.1090/bull/1635 10.1090/S0002-9904-1942-07615-4
ContentType	Journal Article
Copyright	2022 Elsevier Inc. Copyright American Elsevier Company, Inc. Jul 15, 2022
Copyright_xml	– notice: 2022 Elsevier Inc. – notice: Copyright American Elsevier Company, Inc. Jul 15, 2022
DBID	AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D
DOI	10.1016/j.laa.2022.03.007
DatabaseName	CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional
DatabaseTitle	CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional
DatabaseTitleList	Computer and Information Systems Abstracts
DeliveryMethod	fulltext_linktorsrc
Discipline	Mathematics
EISSN	1873-1856
EndPage	67
ExternalDocumentID	10_1016_j_laa_2022_03_007 S0024379522001021
GroupedDBID	--K --M --Z -~X .~1 0R~ 1B1 1RT 1~. 1~5 4.4 457 4G. 5GY 6TJ 7-5 71M 8P~ 9JN AACTN AAEDW AAIKJ AAKOC AALRI AAOAW AAQFI AASFE AATTM AAXKI AAXUO ABAOU ABJNI ABMAC ACDAQ ACGFS ACRLP ADBBV ADEZE AEBSH AEIPS AEKER AENEX AFTJW AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AKRWK ALMA_UNASSIGNED_HOLDINGS AMRAJ ANKPU ARUGR AXJTR BKOJK BLXMC BNPGV CS3 DU5 EBS EFJIC EO8 EO9 EP2 EP3 F5P FDB FEDTE FIRID FNPLU FYGXN G-Q GBLVA HVGLF IHE IXB J1W KOM M26 M41 MCRUF MHUIS MO0 N9A O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 RNS ROL RPZ SDF SDG SES SPC SPCBC SSH SSW T5K TN5 TWZ WH7 XPP YQT ZMT ~G- 29L 5VS 9DU AAEDT AAQXK AAYWO AAYXX ABDPE ABEFU ABFNM ABWVN ABXDB ACLOT ACRPL ACVFH ADCNI ADIYS ADMUD ADNMO ADVLN AETEA AEUPX AEXQZ AFFNX AFJKZ AFPUW AGHFR AGQPQ AIGII AIIUN AKBMS AKYEP APXCP ASPBG AVWKF AZFZN CITATION EFKBS EFLBG EJD FA8 FGOYB G-2 HZ~ MVM OHT R2- SEW SSZ T9H WUQ ~HD 7SC 8FD JQ2 L7M L~C L~D
ID	FETCH-LOGICAL-c255t-9b70f4d956937c75ca5a2993209213a1bb6ae1312659a9504804c54d00d79d293
ISICitedReferencesCount	7
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000806350200004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0024-3795
IngestDate	Sun Nov 30 04:49:53 EST 2025 Sat Nov 29 07:30:36 EST 2025 Tue Nov 18 22:25:13 EST 2025 Sun Apr 06 06:54:15 EDT 2025
IsPeerReviewed	true
IsScholarly	true
Keywords	Lineability 12J99 Linear function Strongly everywhere surjective 46S10 46B87 Normed space 15A03 Field Everywhere surjective Topological vector space Discontinuous function Absolute value
Language	English
LinkModel	OpenURL
MergedId	FETCHMERGED-LOGICAL-c255t-9b70f4d956937c75ca5a2993209213a1bb6ae1312659a9504804c54d00d79d293
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0002-1016-096X
PQID	2704305609
PQPubID	2047554
PageCount	16
ParticipantIDs	proquest_journals_2704305609 crossref_primary_10_1016_j_laa_2022_03_007 crossref_citationtrail_10_1016_j_laa_2022_03_007 elsevier_sciencedirect_doi_10_1016_j_laa_2022_03_007
PublicationCentury	2000
PublicationDate	2022-07-15
PublicationDateYYYYMMDD	2022-07-15
PublicationDate_xml	– month: 07 year: 2022 text: 2022-07-15 day: 15
PublicationDecade	2020
PublicationPlace	Amsterdam
PublicationPlace_xml	– name: Amsterdam
PublicationTitle	Linear algebra and its applications
PublicationYear	2022
Publisher	Elsevier Inc American Elsevier Company, Inc
Publisher_xml	– name: Elsevier Inc – name: American Elsevier Company, Inc
References	Fernández-Sánchez, Maghsoudi, Rodríguez-Vidanes, Seoane-Sepúlveda (br0100) 2022; 116 Gámez-Merino, Muñoz Fernández, Sánchez, Seoane-Sepúlveda (br0190) 2010; 138 Ciesielski, Seoane-Sepúlveda (br0080) 2019; 56 Gurariy, Quarta (br0090) 2004; 294 Fenoy-Muñoz, Gámez-Merino, Muñoz Fernández, Sáez-Maestro (br0120) 2017; 15 Aczél, Dhombres (br0200) 1989; vol. 31 Robert (br0130) 2000; vol. 198 Jech (br0170) 2003 Köthe (br0150) 1979; vol. 237 Bernal-González, Pellegrino, Seoane-Sepúlveda (br0050) 2014; 51 García-Pacheco, Palmberg, Seoane-Sepúlveda (br0010) 2007; 326 Aron, Gurariy, Seoane (br0040) 2005; 133 Köthe (br0140) 1969; Band 159 Jones (br0020) 1942; 48 Seoane-Sepúlveda (br0070) 2006 Aizpuru, Pérez-Eslava, Seoane-Sepúlveda (br0030) 2006; 418 Hodel (br0160) 1984 García-Pacheco, Rambla-Barreno, Seoane-Sepúlveda (br0110) 2008; 102 Aron, Bernal González, Pellegrino, Seoane Sepúlveda (br0060) 2016 Fichtenholz, Kantorovich (br0180) 1934; 5 Gámez-Merino (10.1016/j.laa.2022.03.007_br0190) 2010; 138 Robert (10.1016/j.laa.2022.03.007_br0130) 2000; vol. 198 Aczél (10.1016/j.laa.2022.03.007_br0200) 1989; vol. 31 Aizpuru (10.1016/j.laa.2022.03.007_br0030) 2006; 418 Ciesielski (10.1016/j.laa.2022.03.007_br0080) 2019; 56 Jones (10.1016/j.laa.2022.03.007_br0020) 1942; 48 Gurariy (10.1016/j.laa.2022.03.007_br0090) 2004; 294 Jech (10.1016/j.laa.2022.03.007_br0170) 2003 Fichtenholz (10.1016/j.laa.2022.03.007_br0180) 1934; 5 García-Pacheco (10.1016/j.laa.2022.03.007_br0010) 2007; 326 García-Pacheco (10.1016/j.laa.2022.03.007_br0110) 2008; 102 Fenoy-Muñoz (10.1016/j.laa.2022.03.007_br0120) 2017; 15 Köthe (10.1016/j.laa.2022.03.007_br0150) 1979; vol. 237 Bernal-González (10.1016/j.laa.2022.03.007_br0050) 2014; 51 Fernández-Sánchez (10.1016/j.laa.2022.03.007_br0100) 2022; 116 Aron (10.1016/j.laa.2022.03.007_br0040) 2005; 133 Köthe (10.1016/j.laa.2022.03.007_br0140) 1969; Band 159 Aron (10.1016/j.laa.2022.03.007_br0060) 2016 Seoane-Sepúlveda (10.1016/j.laa.2022.03.007_br0070) 2006 Hodel (10.1016/j.laa.2022.03.007_br0160) 1984
References_xml	– volume: 418 start-page: 595 year: 2006 end-page: 598 ident: br0030 article-title: Linear structure of sets of divergent sequences and series publication-title: Linear Algebra Appl. – volume: 56 start-page: 211 year: 2019 end-page: 260 ident: br0080 article-title: Differentiability versus continuity: restriction and extension theorems and monstrous examples publication-title: Bull. Am. Math. Soc. (N.S.) – volume: 138 start-page: 3863 year: 2010 end-page: 3876 ident: br0190 article-title: Sierpiński-Zygmund functions and other problems on lineability publication-title: Proc. Am. Math. Soc. – volume: 326 start-page: 929 year: 2007 end-page: 939 ident: br0010 article-title: Lineability and algebrability of pathological phenomena in analysis publication-title: J. Math. Anal. Appl. – year: 2016 ident: br0060 article-title: Lineability: The Search for Linearity in Mathematics publication-title: Monographs and Research Notes in Mathematics – volume: vol. 198 year: 2000 ident: br0130 article-title: A Course in publication-title: Graduate Texts in Mathematics – volume: 51 start-page: 71 year: 2014 end-page: 130 ident: br0050 article-title: Linear subsets of nonlinear sets in topological vector spaces publication-title: Bull. Am. Math. Soc. (N.S.) – volume: 15 start-page: 486 year: 2017 end-page: 501 ident: br0120 article-title: A hierarchy in the family of real surjective functions publication-title: Open Math. – volume: vol. 237 year: 1979 ident: br0150 article-title: Topological Vector Spaces. II publication-title: Grundlehren der Mathematischen Wissenschaften – volume: Band 159 year: 1969 ident: br0140 article-title: Topological Vector Spaces. I publication-title: Die Grundlehren der Mathematischen Wissenschaften – volume: 5 start-page: 69 year: 1934 end-page: 98 ident: br0180 article-title: Sur les opérations dans l'espace des functions bornées publication-title: Stud. Math. – start-page: 1 year: 1984 end-page: 61 ident: br0160 article-title: Cardinal functions. I publication-title: Handbook of Set-Theoretic Topology – volume: 294 start-page: 62 year: 2004 end-page: 72 ident: br0090 article-title: On lineability of sets of continuous functions publication-title: J. Math. Anal. Appl. – volume: vol. 31 year: 1989 ident: br0200 article-title: Functional Equations in Several Variables publication-title: Encyclopedia of Mathematics and Its Applications – volume: 48 start-page: 115 year: 1942 end-page: 120 ident: br0020 article-title: Connected and disconnected plane sets and the functional equation publication-title: Bull. Am. Math. Soc. – volume: 133 start-page: 795 year: 2005 end-page: 803 ident: br0040 article-title: Lineability and spaceability of sets of functions on publication-title: Proc. Am. Math. Soc. – volume: 116 year: 2022 ident: br0100 article-title: Classical vs. non-Archimedean analysis: an approach via algebraic genericity publication-title: Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. – year: 2003 ident: br0170 article-title: Set Theory publication-title: Springer Monographs in Mathematics – year: 2006 ident: br0070 article-title: Chaos and lineability of pathological phenomena in analysis – volume: 102 start-page: 156 year: 2008 end-page: 160 ident: br0110 article-title: -linear functions, functions with dense graph, and everywhere surjectivity publication-title: Math. Scand. – volume: 5 start-page: 69 year: 1934 ident: 10.1016/j.laa.2022.03.007_br0180 article-title: Sur les opérations dans l'espace des functions bornées publication-title: Stud. Math. doi: 10.4064/sm-5-1-69-98 – volume: 116 issue: 2 year: 2022 ident: 10.1016/j.laa.2022.03.007_br0100 article-title: Classical vs. non-Archimedean analysis: an approach via algebraic genericity publication-title: Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. – start-page: 1 year: 1984 ident: 10.1016/j.laa.2022.03.007_br0160 article-title: Cardinal functions. I – volume: 326 start-page: 929 issue: 2 year: 2007 ident: 10.1016/j.laa.2022.03.007_br0010 article-title: Lineability and algebrability of pathological phenomena in analysis publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2006.03.025 – volume: 138 start-page: 3863 issue: 11 year: 2010 ident: 10.1016/j.laa.2022.03.007_br0190 article-title: Sierpiński-Zygmund functions and other problems on lineability publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-2010-10420-3 – volume: 418 start-page: 595 issue: 2–3 year: 2006 ident: 10.1016/j.laa.2022.03.007_br0030 article-title: Linear structure of sets of divergent sequences and series publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2006.02.041 – volume: 102 start-page: 156 issue: 1 year: 2008 ident: 10.1016/j.laa.2022.03.007_br0110 article-title: Q-linear functions, functions with dense graph, and everywhere surjectivity publication-title: Math. Scand. doi: 10.7146/math.scand.a-15057 – volume: vol. 237 year: 1979 ident: 10.1016/j.laa.2022.03.007_br0150 article-title: Topological Vector Spaces. II – volume: 294 start-page: 62 issue: 1 year: 2004 ident: 10.1016/j.laa.2022.03.007_br0090 article-title: On lineability of sets of continuous functions publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2004.01.036 – volume: vol. 31 year: 1989 ident: 10.1016/j.laa.2022.03.007_br0200 article-title: Functional Equations in Several Variables – year: 2003 ident: 10.1016/j.laa.2022.03.007_br0170 article-title: Set Theory – volume: Band 159 year: 1969 ident: 10.1016/j.laa.2022.03.007_br0140 article-title: Topological Vector Spaces. I – volume: 51 start-page: 71 issue: 1 year: 2014 ident: 10.1016/j.laa.2022.03.007_br0050 article-title: Linear subsets of nonlinear sets in topological vector spaces publication-title: Bull. Am. Math. Soc. (N.S.) doi: 10.1090/S0273-0979-2013-01421-6 – volume: 15 start-page: 486 issue: 1 year: 2017 ident: 10.1016/j.laa.2022.03.007_br0120 article-title: A hierarchy in the family of real surjective functions publication-title: Open Math. doi: 10.1515/math-2017-0042 – volume: 133 start-page: 795 issue: 3 year: 2005 ident: 10.1016/j.laa.2022.03.007_br0040 article-title: Lineability and spaceability of sets of functions on R publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-04-07533-1 – year: 2006 ident: 10.1016/j.laa.2022.03.007_br0070 article-title: Chaos and lineability of pathological phenomena in analysis – volume: vol. 198 year: 2000 ident: 10.1016/j.laa.2022.03.007_br0130 article-title: A Course in p-Adic Analysis – year: 2016 ident: 10.1016/j.laa.2022.03.007_br0060 article-title: Lineability: The Search for Linearity in Mathematics – volume: 56 start-page: 211 issue: 2 year: 2019 ident: 10.1016/j.laa.2022.03.007_br0080 article-title: Differentiability versus continuity: restriction and extension theorems and monstrous examples publication-title: Bull. Am. Math. Soc. (N.S.) doi: 10.1090/bull/1635 – volume: 48 start-page: 115 year: 1942 ident: 10.1016/j.laa.2022.03.007_br0020 article-title: Connected and disconnected plane sets and the functional equation f(x)+f(y)=f(x+y) publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0002-9904-1942-07615-4
SSID	ssj0004702
Score	2.373802
Snippet	It is well known that there are Q-linear discontinuous functions from R to R. Moreover, such functions have dense graph in the real plane. In this paper, we... It is well known that there are R to R. Moreover, such functions have dense graph in the real plane. In this paper, we study the existence of linear spaces...
SourceID	proquest crossref elsevier
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	52
SubjectTerms	Absolute value Discontinuous function Everywhere surjective Field Lineability Linear algebra Linear function Normed space Strongly everywhere surjective Topological vector space Vector spaces
Title	Lineability and K-linear discontinuous functions
URI	https://dx.doi.org/10.1016/j.laa.2022.03.007 https://www.proquest.com/docview/2704305609
Volume	645
WOSCitedRecordID	wos000806350200004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1873-1856 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0004702 issn: 0024-3795 databaseCode: AIEXJ dateStart: 20211212 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELZWWw5wQDxFoaAcOIEcOY4dx8ctLYICFdIusDfLSRy0q1W62pf6K_qbO46dB4ta0QOXKLLGVuyZ2PPyNwi9jYXUacE51llZYsZNhHWiNS4TC4ubiUSXui42Ic7P0-lUfh8Mrpq7MLuFqKr08lIu_yuroQ2Yba_O3oHd7aDQAO_AdHgC2-H5T4wH69I48G0HrfQFW01Sr2wsxiamz6qtTXu1B1rnrJv3-q7e29ofYEW3gYV-lLvvgK6j7JH1QuOxfwcZqF3SZ2EXyilcOP7k9xYIf84K7csDnIRfW6qxuYBmPDZLS3s8WuxM4dJ4w-OWaLLabtYWc7ben36FfZcFrdNb3aXN9goBg53NVddstuGE8d5G6mBt_ZHsCnb8tdk7v8M8XGgLIEWpQ6sV3cnWRPP3Drw2DbHJcJsrGELZIRSJVQ1OcEAFl-kQHYw-n07Pupu2gnj8eTeBJk5eZwzufcdNms7emV8rMpNH6KG3QIKRk5zHaGCqJ-jBtxa-d_0UkZ4MBSAEQSNDwR8yFLQy9Az9-Hg6-fAJ-9IaOAcbcoNlJkjJCjCOQT3NBc8116CYxJRIGsU6yrJEmyiOaMKlltwCD7Ccs4KQQsgCVMTnaFhdVOYFCtIkpgLsDEaoZHnBdEQLYkpTRpkUeVYeItIsg8o97rwtf7JQNy7_IXrXdlk60JXbiFmztsprjU4bVCAnt3U7avig_N-7VjARC4GXEPnyLp_wCt3vxPwIDTerrXmN7uW7zWy9euNl6Bq3b5GV
linkProvider	Elsevier
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Lineability+and+K-linear+discontinuous+functions&rft.jtitle=Linear+algebra+and+its+applications&rft.au=Fern%C3%A1ndez-S%C3%A1nchez%2C+J.&rft.au=Rodr%C3%ADguez-Vidanes%2C+D.L.&rft.au=Seoane-Sep%C3%BAlveda%2C+J.B.&rft.au=Trutschnig%2C+W.&rft.date=2022-07-15&rft.issn=0024-3795&rft.volume=645&rft.spage=52&rft.epage=67&rft_id=info:doi/10.1016%2Fj.laa.2022.03.007&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_laa_2022_03_007
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0024-3795&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0024-3795&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0024-3795&client=summon