Set Theoretic Topology Seminar

Speaker: Ziqin Feng

Title:  Countable Tightness of Free Topological Groups

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. For every \(n\in\mathbb{N}\), \(F_{n}(X)\) (\(A_n(X)\)) denotes the subspace of \(F(X)\) (respectively, \(A(X)\)) that consists of all words of reduced length at most \(n\) with respect to the free basis \(X\). The subspace \(A_{n}(X)\) is defined similarly.

Jointly with Dr. Fucai Lin and Dr. Chuan Liu, we prove the following results: 

(2) Let \(X\) be the closed image of locally separable metrizable space. Then \(A_4(X)\) is of countable tightness if and only if \(A(X)\) is of countable tightness.