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.