Countable tightness and \mathfrak G-bases on Free topological groups

2015/12/23 by Fucai Lin, Lin, Fucai, Alex Ravsky +3
Mathematics · #Advanced Topology and Set Theory #Rings, Modules, and Algebras #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1512.07515

Abstract

Given a Tychonoff space X, let F(X) and A(X) be respectively the free topological group and the free Abelian topological group over X in the sense of Markov. In this paper, we consider two topological properties of F(X) or A(X), namely the countable tightness and \mathfrak G-base. We provide some characterizations of the countable tightness and \mathfrak G-base of F(X) and A(X) for various special classes of spaces X. Furthermore, we also study the countable tightness and \mathfrak G-base of some F_n(X) of F(X).

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