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# Topology - Set-Theoretic

**DMS Set Theoretic Topology Seminar**

Oct 10, 2018 02:00 PM

Parker Hall 328

Speaker: **Rongxin Shen**

Abstract. This is joint work with Heikki Junnila. The notion of a reflexive family of sets in topological spaces originated in research on the invariant subspace problem in functional analysis. In [Fund. Math., 192 (2006), 111--120], Yang and Zhao introduced the s-reflexive spaces in which reflexive families can be characterized in a simple way. We prove that every s-reflexive Hausdorff space is zero-dimensional, and we indicate a close relationship between the theory of s-reflexive spaces and that of continuous selections. Several examples relating to s-reflexivity are given. Also we will talk about some unsolved problems on this topic.

**DMS Set Theoretic Topology Seminar**

Sep 19, 2018 02:00 PM

Parker Hall 328

**Gary Gruenhage**will continue presenting the paper of Dow and Juhasz.

**DMS Set Theoretic Topology Seminar**

Sep 12, 2018 02:00 PM

Parker Hall 328

**Hongfeng Guo** will show that there is a monotonically monolithic space which has no predictable network under the assumption \(2^{\omega_0}<2^{\omega_1}\).

This is joint work with Ziqin Feng.

**DMS Set Theoretic Topology Seminar**

Sep 05, 2018 02:00 PM

Parker Hall 328

Speaker: **Gary Gruenhage**

Topic: continues presenting the paper of Dow and Juhasz

**DMS Set Theoretic Topology Seminar**

Aug 29, 2018 02:00 PM

Parker Hall 328

NOTICE THE UNUSUAL ROOM!

Speaker: **Gary Gruenhage**

Topic: He will present a paper of Dow and Juhasz which is related to a problem he is interested in.

**DMS Set Theoretic Topology Seminar**

Apr 18, 2018 02:00 PM

Parker Hall 246

Speaker:

**Alex Shibakov**, Tennessee Technological University

Title: Convergence in the presence of group structure: Problems, new and old

**DMS Set Theoretic Topology Seminar**

Mar 28, 2018 02:00 PM

Parker Hall 246

Speaker: **Rongxin Shen**, one of our visitors from China

Title: Generalized metrizable properties in topological algebra

**DMS Set Theoretic Topology Seminar**

Mar 21, 2018 02:00 PM

Parker Hall 249

Note: New Room for this week (PH 249)

Speaker: **Mike Reed**, St Edmund Hall, Oxford University

Title: Open Questions Concerning Compactness Conditions in Moore Spaces

Abstract: All spaces are considered to be regular and T_1.

**Definition.** A space **S **is 1-starcompact if for each open covering **U** of **S,** there exists a finite subcollection **V **of **U **such that each member of **U **has non-empty intersection with a member of **V**.

**Questions. **

1. In ZFC, is each 1-starcompact Moore space compact?

2. In ZFC, does there exist a first countable, 1-starcompact space that is not countable compact?

3. In ZFC, is each normal, separable Moore space Scott-representable?

4. In ZFC, does there exist a cwH Moore space that is not cwn with respect to compact sets?

5. Is there a consistent with ZFC example of a normal, locally compact, separable Moore space **S **such that the square of **S **is not normal?

The speaker presents construction techniques relevant to these open questions.

**DMS Set Theoretic Topology Seminar**

Mar 07, 2018 02:00 PM

Parker Hall 246

Speaker: **Professor Huaipeng Chen**, one of our visitors from China

Title: A stratifiable space which is not \(M_1\).

Huaipeng will outline his idea for a possible example with the properties of the title. If the example is correct, it would solve a 57-year-old problem in general topology.

**DMS Set Theoretic Topology Seminar**

Feb 21, 2018 02:00 PM

Parker Hall 246

Speaker: **Ziqin Feng** will continue (and finish)

Title: Seeking a Network Characterization of Corson Compacta.

Abstract: We will identify a characterization of Corson Compacta using base and point networks. This provides an answer to a question raised by A. Dow, H. Junnila, and J. Pelant, also by F. Garcia, L. Oncina, and J. Orihuela in their articles.

Last Updated: 09/11/2015