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
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.
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页码:149 / 156
页数:8
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