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# Topology - Set-Theoretic

DMS Set Theoretic Topology Seminar
Jan 16, 2019 02:00 PM
Parker Hall 246 (New Room)

Speaker: Gary Gruenhage

Abstract.  A space X is said to be Y-selective if every lower semi-continuous mapping F from the space Y to the non-empty closed subsets of X has a continuous selection, i.e., there is a continuous f from Y to X with f(y) in F(y) for each y in Y.   X is self-selective if it is X-selective.  R. Shen and H.J.K. Junnila asked if the space of ordinals less than or equal to the first uncountable ordinal is self-selective.  We show that it is not.

DMS Set Theoretic Topology Seminar
Dec 05, 2018 02:00 PM
Parker Hall 328

Speaker: Ziqin Feng will continue his talk from 11/14 (and finish, as tomorrow is our last meeting of the semester).

DMS Set Theoretic Topology Seminar
Nov 14, 2018 02:00 PM
Parker Hall 328

Speaker: Xiqin Feng
DMS Set Theoretic Topology Seminar
Nov 07, 2018 02:00 PM
Parker Hall 328

Mark will continue

Abstract.  In 1979, van Douwen and Pfeffer introduced D-spaces and showed every finite power of the Sorgenfrey line is a D-space. Two years later, de Caux proved that every finite power of the Sorgenfrey line is hereditarily a D-space. Peng introduced the notion of transitively D-spaces in 2008, and Dauvergne demonstrated in 2016 that a transitively D-space need not be a D-space. We build on de Caux's technique to show every finite power of a GO-topology on the reals is hereditarily a transitively D-space.

DMS Set Theoretic Topology Seminar
Oct 31, 2018 02:00 PM
Parker Hall 328

Mark will continue.

Abstract.  In 1979, van Douwen and Pfeffer introduced D-spaces and showed every finite power of the Sorgenfrey line is a D-space. Two years later, de Caux proved that every finite power of the Sorgenfrey line is hereditarily a D-space. Peng introduced the notion of transitively D-spaces in 2008, and Dauvergne demonstrated in 2016 that a transitively D-space need not be a D-space. We build on de Caux's technique to show every finite power of a GO-topology on the reals is hereditarily a transitively D-space.

DMS Set Theoretic Topology Seminar
Oct 24, 2018 02:00 PM
Parker Hall 328

Speaker: Mark Guest

Abstract.  In 1979, van Douwen and Pfeffer introduced D-spaces and showed every finite power of the Sorgenfrey line is a D-space. Two years later, de Caux proved that every finite power of the Sorgenfrey line is hereditarily a D-space. Peng introduced the notion of transitively D-spaces in 2008, and Dauvergne demonstrated in 2016 that a transitively D-space need not be a D-space. We build on de Caux's technique to show every finite power of a GO-topology on the reals is hereditarily a transitively D-space.

DMS Set Theoretic Topology Seminar
Oct 17, 2018 02:00 PM
Parker Hall 328

Rongxin will continue

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.

Last Updated: 09/11/2015