The $k_{R}$-property on free topological groups

Fucai Lin; Shou Lin; Chuan Liu

The $k_{R}$-property on free topological groups

Group Theory 2017-06-08 v2 Functional Analysis General Topology

Authors: Fucai Lin , Shou Lin , Chuan Liu

Abstract

A space $X$ is called a $k_{R}$ -space, if $X$ is Tychonoff and the necessary and sufficient condition for a real-valued function $f$ on $X$ to be continuous is that the restriction of $f$ on each compact subset is continuous. In this paper, we mainly discuss the $k_{R}$ -property on the free topological groups, and generalize some well-known results of K. Yamada's in the free topological groups.

Keywords

free topological groups k_R-space Tychonoff space real-valued function compact subset continuity

Cite

@article{arxiv.1610.02523,
  title  = {The $k_{R}$-property on free topological groups},
  author = {Fucai Lin and Shou Lin and Chuan Liu},
  journal= {arXiv preprint arXiv:1610.02523},
  year   = {2017}
}

Comments

9 pages. arXiv admin note: substantial text overlap with arXiv:1610.02522

The $k_{R}$-property on free topological groups

Abstract

Keywords

Cite

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