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# Topology - Set-Theoretic

DMS special conference in set-theoretic topology, which is in honor of Professor Gary Gruenhage’s 70th birthday
Oct 20, 2017 01:20 PM
Haley Center 1403 (Fri) Parker Hall 249 (Sat-Sun)

for all details

DMS Set Theoretic Topology Seminar
Oct 15, 2017 04:00 PM
Parker Hall 224

Ziqin will continue.

Title: Spaces with -dominated diagonal

Abstract:  A space is dominated by if there is a -directed compact cover, where is the set of compact subsets of the space .   We will show that, under , a compact space with a -dominated diagonal is metrizable (where is the space of rational numbers).

DMS Set Theoretic Topology Seminar
Oct 09, 2017 04:00 PM
Parker Hall 224

Ziqin will continue.

Title: Spaces with $$\mathbb{Q}$$-dominated diagonal

Abstract:  A space is dominated by $$M$$ if there is a $$\mathcal{K}(M)$$-directed compact cover, where $$\mathcal{K}(M)$$ is the set of compact subsets of the space $$M$$.   We will show that, under $$\mathfrak{b}>\omega_1$$, a compact space with a $$\mathbb{Q}$$-dominated diagonal is metrizable (where $$\mathbb{Q}$$ is the space of rational numbers).

DMS Set Theoretic Topology Seminar
Sep 25, 2017 04:00 PM
Parker Hall 224

Speaker: Ziqin Feng will continue at 4 (NOTE THE TIME CHANGE!).

Title: Spaces with $$\mathbb{Q}$$-dominated diagonal

DMS Set Theoretic Topology Seminar
Sep 18, 2017 03:00 PM
Parker Hall 224

Speaker: Ziqin Feng ﻿continues

Title: Spaces with $$\mathbb{Q}$$-dominated diagonal

Abstract:  A space is dominated by $$M$$ if there is a $$\mathcal{K}(M)$$-directed compact cover, where $$\mathcal{K}(M)$$ is the set of compact subsets of the space $$M$$.   We will show that, under $$\mathfrak{b}>\omega_1$$, a compact space with a $$\mathbb{Q}$$-dominated diagonal is metrizable (where $$\mathbb{Q}$$ is the space of rational numbers).

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DMS Set Theoretic Topology Seminar
Aug 28, 2017 03:00 PM
Parker Hall 224

Speaker: Ziqin Feng

Title: Spaces with $$\mathbb{Q}$$-dominated diagonal

Abstract:  A space is dominated by $$M$$ if there is a $$\mathcal{K}(M)$$-directed compact cover, where $$\mathcal{K}(M)$$ is the set of compact subsets of the space $$M$$.   We will show that, under $$\mathfrak{b}>\omega_1$$, a compact space with a $$\mathbb{Q}$$-dominated diagonal is metrizable (where $$\mathbb{Q}$$ is the space of rational numbers).

Set Theoretic Topology Seminar
Apr 24, 2017 04:00 PM
Parker Hall 228

Joel Alberto Aguilar

Title: On Dense subspaces of countable pseudocharacter in function spaces (II)

Abstract: A space is $\psi$-separable if it has a dense subspace with countable pseudocharacter. We are going to prove that if $X$ is an infinite space and there exists a subspace with countable pseudocharacter $T\subset X\times X$ and $|T|\geq iw(X)$, then $C_{p}(X)$ is $\psi$-separable. We are also going to give an improvement on the fact that if $X$ is Corson compact, then $C_{p}(X)$ has a dense $\sigma$-discrete subpace.

This will be our last set-theoretic seminar for this semester.

Set Theoretic Topology Seminar
Apr 17, 2017 04:00 PM
Parker Hall 228

Speaker: Joel Alberto Aguilar

Title: On Dense subspaces of countable pseudocharacter in function spaces (II)

Abstract: A space is $\psi$-separable if it has a dense subspace with countable pseudocharacter. We are going to prove that if $X$ is an infinite space and there exists a subspace with countable pseudocharacter $T\subset X\times X$ and $|T|\geq iw(X)$, then $C_{p}(X)$ is $\psi$-separable. We are also going to give an improvement on the fact that if $X$ is Corson compact, then $C_{p}(X)$ has a dense $\sigma$-discrete subpace.

Set Theoretic Topology Seminar
Apr 10, 2017 04:00 PM
Parker Hall 228

Ziqin Feng continues

Title:  Countable Tightness of Free Topological Groups (II)

Set Theoretic Topology Seminar
Apr 03, 2017 04:00 PM
Parker Hall 228

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.

Set Theoretic Topology Seminar
Mar 20, 2017 04:00 PM
Parker Hall 228

Speaker: Alex Shibakov

Title:  Gaps in convergence and the Cohen reals

Abstract.  I will present a model in which all countable sequential groups have trivial sequential orders and there exists an uncountable sequential group of an intermediate sequential order.

Last Updated: 09/11/2015