COSAM » Events » 2017 » April » Set Theoretic Topology Seminar

 Set Theoretic Topology Seminar Time: Apr 03, 2017 (04:00 PM) Location: Parker Hall 228 Details: 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:  (1) Assume $$\mathfrak{b}=\omega_1$$. For a non-metrizable Lašnev space $$X$$, $$F_5(X)$$ is of countable tightness if and only if $$F(X)$$ is of countable tightness; (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.

Last updated: 04/03/2017