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...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 645; pp. 52 - 67
Main Authors: Fernández-Sánchez, J., Rodríguez-Vidanes, D.L., Seoane-Sepúlveda, J.B., Trutschnig, W.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 15.07.2022
American Elsevier Company, Inc
Subjects:
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 Access:Get full text
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Summary: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.
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ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2022.03.007