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Free Locally Convex Spaces and the k-space Property

Published online by Cambridge University Press:  20 November 2018

S. S. Gabriyelyan
S. S. Gabriyelyan*
Affiliation:
Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva P.O. 653, Israel e-mail: saak@math.bgu.ac.il
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Abstract

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Let $L\left( X \right)$ be the free locally convex space over a Tychonoff space $X$. Then $L\left( X \right)$ is a $k$-space if and only if $X$ is a countable discrete space. We prove also that $L\left( D \right)$ has uncountable tightness for every uncountable discrete space $D$.

Keywords

46A0354D5054A25free locally convex spacek-spacecountable tightness
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 4 , 01 December 2014 , pp. 803 - 809
Copyright
Copyright © Canadian Mathematical Society 2014

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