Free locally convex spaces and the k-space property

S. S. Gabriyelyan

doi:10.4153/CMB-2014-019-7

Free locally convex spaces and the k-space property

S. S. Gabriyelyan

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Pages (from-to)	803-809
Number of pages	7
Journal	Canadian Mathematical Bulletin
Volume	57
Issue number	4
DOIs	https://doi.org/10.4153/CMB-2014-019-7
State	Published - 1 Dec 2014

Keywords

Countable tightness
Free locally convex space
K-space

All Science Journal Classification (ASJC) codes

General Mathematics

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10.4153/CMB-2014-019-7

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title = "Free locally convex spaces and the k-space property",

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.",

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AB - 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.

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Free locally convex spaces and the k-space property

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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