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# Topology - Set-Theoretic

**DMS Topology Seminar**

Jan 18, 2023 01:00 PM

224 Parker Hall

Speaker: **Arka Banerjee** Title: Coarse cohomology of the complement Abstract: John Roe defined the notion of Coarse cohomology of a metric space that measures the behavior at infinity of a space: more specifically, it measures the way in which uniformly large bounded sets fit together. In my talk I will give a brief introduction to this theory and define a new notion called "Coarse cohomology of the complement." Time permitting, I will discuss some related results and applications.

This talk is partly based on a joint work with Boris Okun.

**DMS Topology Seminar**

Nov 18, 2022 02:00 PM

224 Parker Hall and ZOOM

Speaker: **Steven Clontz**, University of South Alabama Title: Metrizability of Mahavier products indexed by partial orders

Abstract: Let $X$ be separable metrizable, and let $f\subseteq X^2$ be a non-trivial relation on $X$. For a given partial order $(P,\leq)$, the Mahavier product $M(X,f,P)\subseteq X^P$ (also known as a generalized inverse limit) collects functions such that $x(p)\in f(x(q))$ for all $p<q$. We will show that whenever $f$ satisfies condition $\Gamma$, $M(X,f,P)$ is separable metrizable if and only if $P$ is countable.

**DMS Topology Seminar**

Nov 11, 2022 02:00 PM

ZOOM

Speaker:

**Wlodek Kuperberg**Title: Packing convex bodies in the plane and in space

**DMS Topology Seminar**

Nov 04, 2022 02:00 PM

224 Parker Hall and ZOOM

**PLEASE note NEW DATE**

Speaker: **Michel Smith**

Title: Inverse limits on Hausdorff arcs that are hereditarily indecomposable are metric

Abstract: I will conclude my argument that a hereditarily indecomposable inverse limit of Hausdorff arcs is metric. Note that a Hausdorff arc is a linearly ordered compact connected Hausdorff space and so is not necessarily metric.

**DMS Set Theoretic Topology Seminar**

Mar 06, 2020 02:00 PM

Parker Hall 246

Speaker:

**Professor Vladimir Tkachuk**

Title: Character and tightness are discretely reflexive in compact spaces.

Abstract: We will show that tightness, character, sequentiality, and Frechet-Urysohn property are discretely reflexive in compact spaces, i.e., if \(X\) is a compact space in which the closure of every discrete subset has a property \(P\) from the list \(tightness \leq \kappa, character\leq\kappa, sequentiality, Frechet-Urysohn property\), then \(X\) has the property \(P\).

**DMS Set Theoretic Topology Seminar**

Feb 28, 2020 02:00 PM

Parker Hall 246

Speaker: **Professor Vladimir Tkachuk**

Title: Neither sigma-compactness nor Lindelof Sigma-property is discretely reflexive under CH

Abstract: We will construct, under the Continuum Hypothesis, an example of a space X in which the closure of every discrete set is countable (and hence sigma-compact) while X is not a Lindelof Sigma-space. Therefore, countability, sigma-compactness, and Lindelof Sigma-property all fail to be discretely reflexive under CH.

**DMS Set Theoretic Topology Seminar**

Feb 21, 2020 02:00 PM

Parker Hall 246

Speaker: **Professor Vladimir Tkachuk**

Title: Lindelof property is discretely reflexive in spaces of countable tightness.

Abstract: After finishing the construction of the example of a crowded countable space which is not weakly discretely generated, we will start the proof of discrete reflexivity of the Lindelof property in spaces of countable tightness. In other words, we will prove that if \(X\) is a space of countable tightness and the closure of every discrete subspace of \(X\) is Lindelof, then \(X\) itself is Lindelof. This non-trivial theorem of Arhangel'skii is not easy to prove even for first countable spaces.

**DMS Set Theoretic Topology Seminar**

Feb 14, 2020 02:00 PM

Parker Hall 246

Speaker: **Professor Vladimir Tkachuk**

Title: A countable space need not be weakly discretely generated

Abstract: We will construct a countable crowded Tychonoff space \(X\) in which all discrete subsets are closed. This very non-trivial example of van Douwen shows that a discretely metrizable space is not necessarily first countable or even Frechet-Urysohn. This space has no non-trivial convergent sequences, every dense subspace of \(X\) is open and every nowhere dense subset of \(X\) is closed and discrete.

**DMS Set Theoretic Topology Seminar**

Feb 07, 2020 02:00 PM

Parker Hall 246

Speaker: **Professor Vladimir Tkachuk**

Title: Any monotonically normal space is discretely generated

Abstract: We will give the proof of the statement in the title and start to construct an example of countable crowded space in which every discrete subset is closed. This example shows, among other things, that not all countable spaces are discretely generated.

**DMS Set Theoretic Topology Seminar**

Jan 31, 2020 02:00 PM

Parker Hall 246

Speaker: **Professor Vladimir Tkachuk**

Title: Some nice classes of discretely generated spaces

Abstract: We will see that it is an immediate consequence of discrete reflexivity of compactness that any compact space is weakly discretely generated. The next step will be to establish that any sequential space is discretely generated as well as any compact space of countable tightness. If time permits, I will also prove that any monotonically normal space is discretely generated.

Last Updated: 09/11/2015