2022 Summer Undergraduate Research Program (SURP) Symposium

Location

ScholarSpace, Rod Library, University of Northern Iowa

Presentation Type

Open Access Poster Presentation

Document Type

poster

Abstract

A topological space is left-separated if it can be well-ordered so that every initial segment is closed. Here, we show that all countable ordinal numbers are left-separated. We then prove that a similar method could not work for ω1 , using the pressing-down lemma 1 . We finish by showing that a left-separating well-ordering on ω1 necessarily leads to a contradiction.

Start Date

29-7-2022 11:00 AM

End Date

29-7-2022 1:30 PM

Event Host

Summer Undergraduate Research Program, University of Northern Iowa

Faculty Advisor

Adrienne Stanley

Department

Department of Mathematics

File Format

application/pdf

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Jul 29th, 11:00 AM Jul 29th, 1:30 PM

Left-Separation of ω1

ScholarSpace, Rod Library, University of Northern Iowa

A topological space is left-separated if it can be well-ordered so that every initial segment is closed. Here, we show that all countable ordinal numbers are left-separated. We then prove that a similar method could not work for ω1 , using the pressing-down lemma 1 . We finish by showing that a left-separating well-ordering on ω1 necessarily leads to a contradiction.