The k_R-property on free topological groups

2016/10/08 by Lin, Fucai, Lin, Shou, Liu, Chuan
#22A05 #54D50 #54D55 #54E35 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Group Theory (math.GR) #Primary 54H11 #Secondary 54E20

paper · doi:10.48550/arxiv.1610.02523

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.

Related

• The k_R-property of free Abelian topological groups and products of sequential fans
• The topological properties of q-spaces in free topological groups
• o-Boundedness of free objects over a Tychonoff space
• The k-property and countable tightness of free topological vector spaces
• The k-spaces property of free Abelian topological groups over non-metrizable Lašnev spaces