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: 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. |