2022 Summer Undergraduate Research Program (SURP) Symposium
Location
ScholarSpace, Rod Library, University of Northern Iowa
Presentation Type
Open Access Poster Presentation
Document Type
poster
Keywords
Topological spaces;
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 lemma1 . 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
Copyright
©2022 Lukas Stuelke and Dr. Adrienne Stanley
File Format
application/pdf
Recommended Citation
Stuelke, Lukas and Stanley, Adrienne Ph.D., "Left-Separation of ω1" (2022). Summer Undergraduate Research Program (SURP) Symposium. 28.
https://scholarworks.uni.edu/surp/2022/all/28
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 lemma1 . We finish by showing that a left-separating well-ordering on ω1 necessarily leads to a contradiction.
