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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)

Please see https://sites.google.com/view/auburntopologyconference2017

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).

**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**

**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

**Alex Shibakov**

Last Updated: 09/11/2015