On the property (db) for continuous function spaces
It is shown that the space C( X) of all continuous real-valued functions with the compact-open topology has the property (db) iff X is a μ-space and a τα-space. As a consequence C( X) has the property (db) iff C( X) is Baire-like answering a question in the literature. Generalizations to the topolog...
Uložené v:
| Vydané v: | Topology and its applications Ročník 92; číslo 2; s. 101 - 106 |
|---|---|
| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier B.V
1999
|
| Predmet: | |
| ISSN: | 0166-8641, 1879-3207 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | It is shown that the space
C(
X) of all continuous real-valued functions with the compact-open topology has the property (db) iff
X is a μ-space and a τα-space. As a consequence
C(
X) has the property (db) iff
C(
X) is Baire-like answering a question in the literature. Generalizations to the topology of bounded convergence are given. |
|---|---|
| AbstractList | It is shown that the space
C(
X) of all continuous real-valued functions with the compact-open topology has the property (db) iff
X is a μ-space and a τα-space. As a consequence
C(
X) has the property (db) iff
C(
X) is Baire-like answering a question in the literature. Generalizations to the topology of bounded convergence are given. |
| Author | Render, Hermann |
| Author_xml | – sequence: 1 givenname: Hermann surname: Render fullname: Render, Hermann email: render@math.uni-duisburg.de organization: Gerhard-Mercator-Universität Duisburg, FB 11, 47048 Duisburg, Germany |
| BookMark | eNqFj0tLAzEUhYNUsK3-BGGW7WI0d2aSdHAhUuoDCl2o65DcZDBSkyFJhf57-xAXbrq5Z3O_w_lGZOCDt4RcA70BCvz2dXd4OeMNTFoxpbSqWcnPyBBmoi3riooBGf69XJBRSp-UUmhFNST1yhf5wxZ9DL2NeVtMjJ4WXYgFBp-d34RNKrqNx-yCL1Kv0KZLct6pdbJXvzkm74-Lt_lzuVw9vcwfliXWVOTSUN1QFEIpTaFRLYIAYYABY1ozwymvUGDHuRYCmdICugahrbSBGatR1WNyd-zFGFKKtpPostoPyVG5tQQq9_7y4C_3crIV8uAv-Y5m_-g-ui8Vtye5-yNnd2rfzkaZ0FmP1rhoMUsT3ImGHzIwc_c |
| CitedBy_id | crossref_primary_10_1016_j_topol_2003_12_005 |
| Cites_doi | 10.1215/S0012-7094-58-02523-7 10.1007/BF01431526 10.1016/0166-8641(94)00063-8 10.1007/BF01789479 10.1007/BF01198812 10.1007/BF01200092 |
| ContentType | Journal Article |
| Copyright | 1999 |
| Copyright_xml | – notice: 1999 |
| DBID | 6I. AAFTH AAYXX CITATION |
| DOI | 10.1016/S0166-8641(97)00235-6 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1879-3207 |
| EndPage | 106 |
| ExternalDocumentID | 10_1016_S0166_8641_97_00235_6 S0166864197002356 |
| GroupedDBID | --K --M --Z -~X .~1 0R~ 123 186 1B1 1RT 1~. 1~5 29Q 4.4 457 4G. 5VS 6I. 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AASFE AAXUO ABAOU ABFNM ABJNI ABMAC ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE ADIYS ADMUD AEBSH AEKER AENEX AEXQZ AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HVGLF HZ~ H~9 IHE IXB J1W KOM M26 M41 MCRUF MHUIS MO0 N9A NCXOZ NHB O-L O9- OAUVE OK1 OZT P-8 P-9 PC. Q38 R2- RIG ROL RPZ SCC SDF SDG SES SEW SPC SPCBC SSW SSZ T5K TN5 WH7 WUQ ZKB ~G- 9DU AATTM AAXKI AAYWO AAYXX ABUFD ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD |
| ID | FETCH-LOGICAL-c307t-d0b40c77aab014a9c1717d15155bb5d6062c7cf66b77c5ab71f4c192bd1853ca3 |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000078729800002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0166-8641 |
| IngestDate | Tue Nov 18 22:30:23 EST 2025 Sat Nov 29 07:24:04 EST 2025 Fri Feb 23 02:27:37 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Baire-like spaces db-spaces 54E52 54C35 Continuous function spaces |
| Language | English |
| License | http://www.elsevier.com/open-access/userlicense/1.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c307t-d0b40c77aab014a9c1717d15155bb5d6062c7cf66b77c5ab71f4c192bd1853ca3 |
| OpenAccessLink | https://dx.doi.org/10.1016/S0166-8641(97)00235-6 |
| PageCount | 6 |
| ParticipantIDs | crossref_citationtrail_10_1016_S0166_8641_97_00235_6 crossref_primary_10_1016_S0166_8641_97_00235_6 elsevier_sciencedirect_doi_10_1016_S0166_8641_97_00235_6 |
| PublicationCentury | 1900 |
| PublicationDate | 1999-00-00 |
| PublicationDateYYYYMMDD | 1999-01-01 |
| PublicationDate_xml | – year: 1999 text: 1999-00-00 |
| PublicationDecade | 1990 |
| PublicationTitle | Topology and its applications |
| PublicationYear | 1999 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Todd (BIB14) 1991; 56 Haydon (BIB5) 1973; 276 Buchwalter (BIB3) 1972; 51 Jarchow (BIB7) 1981 Warner (BIB16) 1958; 25 Buchwalter (BIB2) 1969–1970; 9 Husain (BIB6) 1977 Todd, Saxon (BIB15) 1973; 206 Lehner (BIB10) 1979 Kakol (BIB8) 1993; 60 Todd (BIB13) 1981; 21 Blasco (BIB1) 1977; 67 Render (BIB12) 1996; 68 McCoy, Ntantu (BIB11) 1988; 1315 Buchwalter, Schmets (BIB4) 1973; 52 S. Kundu and A.B. Raha, The bounded-open topology and its relatives, Rendiconti dell' Istituto di Matematica dell' Universitá di Trieste, to appear. Todd (10.1016/S0166-8641(97)00235-6_BIB15) 1973; 206 Todd (10.1016/S0166-8641(97)00235-6_BIB14) 1991; 56 Blasco (10.1016/S0166-8641(97)00235-6_BIB1) 1977; 67 McCoy (10.1016/S0166-8641(97)00235-6_BIB11) 1988; 1315 Buchwalter (10.1016/S0166-8641(97)00235-6_BIB3) 1972; 51 Todd (10.1016/S0166-8641(97)00235-6_BIB13) 1981; 21 Warner (10.1016/S0166-8641(97)00235-6_BIB16) 1958; 25 Buchwalter (10.1016/S0166-8641(97)00235-6_BIB4) 1973; 52 Render (10.1016/S0166-8641(97)00235-6_BIB12) 1996; 68 Jarchow (10.1016/S0166-8641(97)00235-6_BIB7) 1981 Buchwalter (10.1016/S0166-8641(97)00235-6_BIB2) 1969; 9 Husain (10.1016/S0166-8641(97)00235-6_BIB6) 1977 10.1016/S0166-8641(97)00235-6_BIB9 Haydon (10.1016/S0166-8641(97)00235-6_BIB5) 1973; 276 Lehner (10.1016/S0166-8641(97)00235-6_BIB10) 1979 Kakol (10.1016/S0166-8641(97)00235-6_BIB8) 1993; 60 |
| References_xml | – year: 1979 ident: BIB10 article-title: Über die Bedeutung gewisser Varianten des Baire'schen Kategorienbegriffs für die Funktionenräume publication-title: Dissertation – volume: 60 start-page: 277 year: 1993 end-page: 282 ident: BIB8 article-title: Sequential closure conditions and Baire-like spaces publication-title: Arch. Math. – year: 1981 ident: BIB7 article-title: Locally Convex Spaces – volume: 21 start-page: 317 year: 1981 end-page: 323 ident: BIB13 publication-title: Annali di Mathematica – volume: 68 start-page: 205 year: 1996 end-page: 239 ident: BIB12 article-title: A nonstandard approach to realcompactness with applications to the equation publication-title: Topology Appl. – volume: 25 start-page: 265 year: 1958 end-page: 282 ident: BIB16 article-title: The topology of compact convergence on continuous function spaces publication-title: Duke Math. J. – volume: 1315 year: 1988 ident: BIB11 article-title: Topological Properties of Spaces of Continuous Functions publication-title: Lectures Notes in Math. – volume: 67 start-page: 179 year: 1977 end-page: 186 ident: BIB1 article-title: On μ-spaces and publication-title: Proc. Amer. Math. Soc. – volume: 9 start-page: 15 year: 1969–1970 ident: BIB2 article-title: Parties bornées d'un espace topologique complètement régulier publication-title: Séminaire Choquet – reference: S. Kundu and A.B. Raha, The bounded-open topology and its relatives, Rendiconti dell' Istituto di Matematica dell' Universitá di Trieste, to appear. – volume: 51 start-page: 399 year: 1972 end-page: 418 ident: BIB3 article-title: Sur le théorème de Nachbin-Shirota publication-title: J. Math. Pures Appl. – volume: 52 start-page: 337 year: 1973 end-page: 352 ident: BIB4 article-title: Sur quelques propriétés de l'espace publication-title: J. Math. Pures Appl. – volume: 206 start-page: 23 year: 1973 end-page: 34 ident: BIB15 article-title: A property of locally convex Baire spaces publication-title: Math. Ann. – year: 1977 ident: BIB6 article-title: Topology and Maps – volume: 56 start-page: 474 year: 1991 end-page: 481 ident: BIB14 article-title: Pseudocompact sets, absolutely Warner bounded sets and continuous function spaces publication-title: Arch. Math. – volume: 276 start-page: 685 year: 1973 end-page: 687 ident: BIB5 article-title: Trois examples dans la théorie des espaces de fonction continues publication-title: C.R. Acad. Sci. Sér. A – volume: 52 start-page: 337 year: 1973 ident: 10.1016/S0166-8641(97)00235-6_BIB4 article-title: Sur quelques propriétés de l'espace Cs(T) publication-title: J. Math. Pures Appl. – year: 1979 ident: 10.1016/S0166-8641(97)00235-6_BIB10 article-title: Über die Bedeutung gewisser Varianten des Baire'schen Kategorienbegriffs für die Funktionenräume Cc(T) – volume: 25 start-page: 265 year: 1958 ident: 10.1016/S0166-8641(97)00235-6_BIB16 article-title: The topology of compact convergence on continuous function spaces publication-title: Duke Math. J. doi: 10.1215/S0012-7094-58-02523-7 – volume: 1315 year: 1988 ident: 10.1016/S0166-8641(97)00235-6_BIB11 article-title: Topological Properties of Spaces of Continuous Functions – volume: 206 start-page: 23 year: 1973 ident: 10.1016/S0166-8641(97)00235-6_BIB15 article-title: A property of locally convex Baire spaces publication-title: Math. Ann. doi: 10.1007/BF01431526 – volume: 9 start-page: 15 year: 1969 ident: 10.1016/S0166-8641(97)00235-6_BIB2 article-title: Parties bornées d'un espace topologique complètement régulier – volume: 276 start-page: 685 year: 1973 ident: 10.1016/S0166-8641(97)00235-6_BIB5 article-title: Trois examples dans la théorie des espaces de fonction continues publication-title: C.R. Acad. Sci. Sér. A – volume: 67 start-page: 179 year: 1977 ident: 10.1016/S0166-8641(97)00235-6_BIB1 article-title: On μ-spaces and kR-spaces – volume: 68 start-page: 205 year: 1996 ident: 10.1016/S0166-8641(97)00235-6_BIB12 article-title: A nonstandard approach to realcompactness with applications to the equation υ(X × Y) = υ(X) × υ(Y) publication-title: Topology Appl. doi: 10.1016/0166-8641(94)00063-8 – volume: 21 start-page: 317 year: 1981 ident: 10.1016/S0166-8641(97)00235-6_BIB13 article-title: Ck(X) and a property of (db)-spaces publication-title: Annali di Mathematica doi: 10.1007/BF01789479 – volume: 51 start-page: 399 year: 1972 ident: 10.1016/S0166-8641(97)00235-6_BIB3 article-title: Sur le théorème de Nachbin-Shirota publication-title: J. Math. Pures Appl. – volume: 60 start-page: 277 year: 1993 ident: 10.1016/S0166-8641(97)00235-6_BIB8 article-title: Sequential closure conditions and Baire-like spaces publication-title: Arch. Math. doi: 10.1007/BF01198812 – volume: 56 start-page: 474 year: 1991 ident: 10.1016/S0166-8641(97)00235-6_BIB14 article-title: Pseudocompact sets, absolutely Warner bounded sets and continuous function spaces publication-title: Arch. Math. doi: 10.1007/BF01200092 – year: 1977 ident: 10.1016/S0166-8641(97)00235-6_BIB6 – year: 1981 ident: 10.1016/S0166-8641(97)00235-6_BIB7 – ident: 10.1016/S0166-8641(97)00235-6_BIB9 |
| SSID | ssj0001972 |
| Score | 1.4809293 |
| Snippet | It is shown that the space
C(
X) of all continuous real-valued functions with the compact-open topology has the property (db) iff
X is a μ-space and a... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 101 |
| SubjectTerms | Baire-like spaces Continuous function spaces db-spaces |
| Title | On the property (db) for continuous function spaces |
| URI | https://dx.doi.org/10.1016/S0166-8641(97)00235-6 |
| Volume | 92 |
| WOSCitedRecordID | wos000078729800002&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: 1879-3207 dateEnd: 20180131 omitProxy: false ssIdentifier: ssj0001972 issn: 0166-8641 databaseCode: AIEXJ dateStart: 19950120 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1JS8QwFA46etCDuOJODh70UJ3ptElzFFFUcAFHmFvJ0oAgmcEZRf-97zVpp8jgcvBS2kLS5Wtf3vo9Qg6YxWpIjLCa1EQJKKxRpts6EiIRNpOWd2y7bDbBb2-zfl_ch850o7KdAHcue38Xw3-FGs4B2Fg6-we460nhBOwD6LAF2GH7K-DvXCh_GgyRNxdVSKPQ-MeEQsxMf3KvmPeKK1oJPsgUHTIJg5ba850TPurIQjPMXYdoyiZ0funCygM3cSAg6UDTm8hYlDHPPFWJQxE3YI8bsq0TvA5FOGJTJbB3BjzUU8NDItevKIl1oims119WozpHsJF-xliOU-VlrBymydksmYs52EItMnd6dd6_rhdf7KLm6dz95SdFWyeTezoU_Cjcz3R1pKFi9JbJUrAN6KnHdIXMFG6VLN7UxLqjNdK9cxQOaYUuPTTqiAKydIIsrZClHtl18nhx3ju7jELfi0iDxB1Hpq2StuZcSgUGrBS6Aza3Qc0zVSo1YHLGmmvLmOJcp1LB_5Ro0NSVQeVLy-4GabmBKzYJVcbIuEi0FWDGS8aEtVmnSJUVaTcV0m6RpHr8XAdSeOxN8px_-_q3yHE9bOhZUX4akFXvNg-qnVfZcvhuvh-6_ddr7ZAFz62BfrJd0hq_vBZ7ZF6_jZ9GL_vhg_kEvGZnUA |
| 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=On+the+property+%28db%29+for+continuous+function+spaces&rft.jtitle=Topology+and+its+applications&rft.au=Render%2C+Hermann&rft.date=1999&rft.issn=0166-8641&rft.volume=92&rft.issue=2&rft.spage=101&rft.epage=106&rft_id=info:doi/10.1016%2FS0166-8641%2897%2900235-6&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_S0166_8641_97_00235_6 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0166-8641&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0166-8641&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0166-8641&client=summon |