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

  • S. S. Gabriyelyan,
    Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva P.O. 653, Israel
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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 free locally convex space, $k$-space, countable tightness
MSC Classifications: 46A03, 54D50, 54A25 show english descriptions General theory of locally convex spaces
$k$-spaces
Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] {For ultrafilters, see 54D80}
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}
 

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