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Topology - Set-Theoretic


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.


DMS Set Theoretic Topology Seminar
Feb 14, 2018 02:00 PM
Parker Hall 246


Speaker: Ziqin Feng will continue
 
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.

DMS Set Theoretic Topology Seminar
Feb 07, 2018 02:00 PM
Parker Hall 246


Speaker: Ziqin Feng

Title: Seeking a Network Characterization of Corson Compacta

Abstract: We will identify a characterization of Corson Compacta using base and point network. 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.


DMS Topology Seminar
Jan 31, 2018 02:00 PM
Parker Hall 246


Speaker: Stu Baldwin

Title: Inverse Limits of Flexagons

Abstract: Flexagons were first introduced in 1939 by Arthur H. Stone when he was a graduate student at Princeton, and they were popularized by Martin Gardner in the December 1956 issue of Scientific American in an article entitled "Flexagons" which launched his well known "Mathematical Games" column, which appeared in that magazine for many years.  By folding strips of paper into various geometrical shapes, Stone created a variety of different flexagons, of which the most elegant are the "hexaflexagons" created by folding strips of equilateral triangles into a hexagonal shape and attaching the ends.

Mathematical studies of flexagons have concentrated on the combinatorial properties of flexagons created with a finite number of polygons.  Here, we consider an infinite version which can be created either using inverse limits or nested intersections of solid tori (viewed as a folded annulus cross the unit interval). If $n \ge 3$, then a strip of $3n$ equilateral triangles can be folded into a hexaflexagon which (after the ends are identified) is topologically an annulus if $n$ is even and a Möbius strip if $n$ is odd.  Of these, the most natural ones are created using $9(2^n)$ triangles, leading to the construction of a space (via either inverse limits or nested intersections) which (viewed as a subset of $\mathbb{R}^3$ in a natural way) mimics the properties of all of the hexaflexagons having finitely many triangles.  Some preliminary results on the properties of this space will be discussed.

 

(Paper toys will be provided to the audience as visual aids.)


DMS Set Theoretic Topology Seminar
Jan 24, 2018 02:00 PM
Parker Hall 246


Postponed due to snow from an earlier date

Speaker: Gary Gruenhage

Topic: A few years ago a researcher in theoretical computer science asked me a question involving the sequential property in (non-Hausdorff) topological spaces.   I will present the example I constructed to answer his question. 


DMS Set Theoretic Topology Seminar
Nov 06, 2017 04:00 PM
Parker Hall 224


Hongfeng will continue
 
Title: The D-property of t-metrizable spaces and their finite unions
 
Abstract: The main results are the following:
1. A t-metrizable space is a D-space.
2. If a space of countable tightness can be written as the union of finite t-metrizable subspaces, then it is a D-space.

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Last Updated: 09/11/2015