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

TL;DR

This paper investigates the $k_{R}$-property in free topological groups, providing generalizations of existing results and characterizing when functions are continuous based on their behavior on compact subsets.

Contribution

It extends the understanding of the $k_{R}$-property within free topological groups and generalizes prior results by K. Yamada.

Findings

Characterization of the $k_{R}$-property in free topological groups

Generalizations of Yamada's results on free topological groups

Conditions under which functions are continuous on these groups

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.