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Topology - Set-Theoretic


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.

DMS Set Theoretic Topology Seminar
Oct 30, 2017 04:00 PM
Parker Hall 224


Speaker: Hongfeng Guo

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.


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

 


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Last Updated: 09/11/2015