location:  Publications → journals → CMB
Abstract view

# Free Locally Convex Spaces and the $k$-space Property

Published:2014-04-15
Printed: Dec 2014
• S. S. Gabriyelyan,
Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva P.O. 653, Israel
 Format: LaTeX MathJax PDF

## Abstract

Let $L(X)$ be the free locally convex space over a Tychonoff space $X$. Then $L(X)$ is a $k$-space if and only if $X$ is a countable discrete space. We prove also that $L(D)$ has uncountable tightness for every uncountable discrete space $D$.
 Keywords: free locally convex space, $k$-space, countable tightness
 MSC Classifications: 46A03 - General theory of locally convex spaces 54D50 - $k$-spaces 54A25 - Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] {For ultrafilters, see 54D80}