TOPOLOGY

Set Theoretic Topology: Mondays, Parker Hall 246, 4:00

Continuum Theory: Mondays, Parker Hall 246, 3:00

SET THEORETIC

April 17             2:30pm in room 249

Speaker: Mike Reed

Title: Open tilings of topological spaces

Mike is a former AU grad in topology (Ben Fitzpatrick was his major professor) who received another PhD in computer science at Oxford U, England.

March 16

Speaker: Ted Porter (former student of Gary G.)

Title: On monotone covering properties

Ted graduated from AU in 2000 and is now full professor at Murray State University in Kentucky.

January 26

Steven Clontz will present some of his results on topological games

December 1

Steven Clontz will continue on his results related to the proximal game of Jocelyn Bell.

November 17

Steven Clontz will speak on his results related to the proximal game of Jocelyn Bell.

November 10

Ana will speak on a new topic.

Title:  Elementary submodels and functions space

October 27

Ana will continue (see below).

October 20

Ana will continue

Title: Tukey order and compact subsets of separable metrizable spaces.

Abstract: Tukey order compares cofinal complexity of partially ordered sets: for posets $P$ and $Q$, $P\geq_T Q$ if and only if there is a map from $P$ to $Q$ taking cofinal subsets of $P$ to cofinal subsets of $Q$. Posets $P$ and $Q$ belong to the same Tukey class if and only if $P\geq_T Q$ and $Q\geq_T P$. In 1965, Isbell asked how many Tukey classes there were among posets of size $\leq \omega_1$. Todor\v{c}evi\'{c} showed in 1985 that the answer is 5' or $2^{\omega_1}$', depending on the set theory. For $2^{\omega_1}$' case he proved that there are $2^{\omega_1}$-many Tukey classes among posets of size $\mathfrak{c}$. So, how many Tukey classes are there among posets of size $\mathfrak{c}$? We will construct, in ZFC, $2^\mathfrak{c}$-sized family of separable metrizable spaces yielding a $2^\mathfrak{c}$-sized antichain of Tukey classes of posets of size $\mathfrak{c}$.

October 13

Ana Mamatelashvili, our new postdoc in topology,  will give several seminar talks beginning today.

Title: Tukey order and compact subsets of separable metrizable spaces.

Abstract: Tukey order compares cofinal complexity of partially ordered sets: for posets $P$ and $Q$, $P\geq_T Q$ if and only if there is a map from $P$ to $Q$ taking cofinal subsets of $P$ to cofinal subsets of $Q$. Posets $P$ and $Q$ belong to the same Tukey class if and only if $P\geq_T Q$ and $Q\geq_T P$. In 1965, Isbell asked how many Tukey classes there were among posets of size $\leq \omega_1$. Todor\v{c}evi\'{c} showed in 1985 that the answer is 5' or $2^{\omega_1}$', depending on the set theory. For $2^{\omega_1}$' case he proved that there are $2^{\omega_1}$-many Tukey classes among posets of size $\mathfrak{c}$. So, how many Tukey classes are there among posets of size $\mathfrak{c}$? We will construct, in ZFC, $2^\mathfrak{c}$-sized family of separable metrizable spaces yielding a $2^\mathfrak{c}$-sized antichain of Tukey classes of posets of size $\mathfrak{c}$.

October 6

Speaker: Max Pitz

Title: Compactifications of w*\{x} and reconstruction of normality

Abstract: I want to speak about the connection between my recent characterisation results of compactifications of w*\{x} under CH, non-normal subspaces of w* and the reconstruction problem for topological spaces.

September 29

Stu Baldwin will continue (and finish) his talk on uniquely homogeneous subsets of R^n.

September 22

Stu Baldwin will continue his talk on uniquely homogeneous subsets of R^n.

September 15

Stu Baldwin continues his talk on uniquely homogeneous subsets of R^n.

September 8

Stu Baldwin will continue his talk on uniquely homogeneous subsets of R^n.

August 25

Stu Baldwin will show us his construction, assuming Martin’s Axiom, of a Uniquely Homogeneous n-1 dimensional subset of R^n. (Martin’s Axiom is a set theoretic axiom weaker than the Continuum Hypothesis; Uniquely Homogeneous means that for any two points x and y in the space, there is one and only one autohomeomorphism of the space which sends x to y.)

CONTINUUM THEORY

April 20

George is scheduled to speak

The slide about germs of continuous functions is omitted, but will something will be sent to those requesting.

April 13

George is scheduled

April 6

CANCELED

March 16

George Kozlowski is presenting today - continuing from Gary’s presentation last week

March 9

Gary Gruenhage will present.

March 2

Krystyna Kuperberg will continue

February 23

Krystyna Kuperberg will present

January 26

Peter has agreed to present first followed by Krystyna.

November 17

Dr. Minc will discuss his joint work with Krasinkiewicz that was referenced in the Hoehn-Oversteegen paper; Dr. K. Kuperberg may discuss the Bing-Jones paper (and how it relates to the Hoehn-Oversteegen result); if time remains, Dr. Smith may discuss some of the techniques due to Bing used in the study of the pseudo-arc.

October 27

We will continue discussing the Hoehn-Oversteegen  homogeneity paper.

October 6

We will continue our examination of the Homogeneity result of Hoehn and Oversteegan.

September 22

Gary Gruenhage will continue with his presentation

September 15

Gary Gruenhage will present some joint results with George Kozlowski and Jan Boronski on 1/k homogeneous nonmetric solenoids.

September 8

Ana Mamatelashvili: Strengthenings of arc-connectedness

Abstract:
A space is said to be n-arc connected if any n points are contained in an arc. I will show that a finite graph is 7-arc connected if and only if it is n-arc connected for every n if and only it is one of the six graphs that we can list out. If there is time I will also consider a further strengthening of this property, namely, requiring any countable set of points to be contained in an arc, and prove that there are only finitely many continua that satisfy this property.

August 25

Piotr Minc: "A weakly chainable uniquely arcwise connected continuum without the fixed point property" by Miroslaw Sobolewski

Last updated: 04/23/2015