On dense-lineability of sets of functions on R

被引：65

作者：

Aron, R. M. ^{[1
]}

Garcia-Pacheco, F. J. ^{[2
]}

Perez-Garcia, D. ^{[3
]}

Seoane-Sepulveda, J. B. ^{[3
]}

机构：

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[3] Univ Complutense Madrid, Dept Anal Matemat, F CC Matemat, E-28040 Madrid, Spain

来源：

TOPOLOGY | 2009年 / 48卷 / 2-4期

关键词：

Lineability; Dense-lineability; Differentiable nowhere monotone functions; SPACES; ALGEBRABILITY; OPERATORS;

D O I：

10.1016/j.top.2009.11.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A subset M of a topological vector space X is said to be dense-lineable in X if there exists an infinite dimensional linear manifold in M boolean OR {0} and dense in X. We give sufficient conditions for a lineable set to be dense-lineable, and we apply them to prove the dense-lineability of several subsets of e[a, b]. We also develop some techniques to show that the set of differentiable nowhere monotone functions is dense-lineable in e[a, b]. Other results related to density and dense-lineability of sets in Banach spaces are also presented. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：149 / 156

页数：8

共 15 条

[1]

[Anonymous], 1952, Journal d'Analyse Mathematique, DOI DOI 10.1007/BF02786968

[2] Lineability and spaceability of sets of functions on R [J].