Dissertations and Theses @ UNI
Availability
Open Access Thesis
Keywords
Numbers; Ordinal; Covering spaces (Topology);
Abstract
William Fleissner and Adrienne Stanley showed that, in finite products of ordinals, the following are equivalent: 1. X is a D-space. 2. X is metacompact. 3. X is metalindel¨of. 4. X does not contain a closed subset which is homeomorphic to a stationary subset of a regular, uncountable cardinal. In this paper we construct a counterexample that shows that this equivalence does not extend to infinite products of ordinals. We also introduce a new property, club-separable, which we show implies D for subsets of ωω1. We hope that club-separable will be able to replace property (4) above in order to generalize the equivalence to infinite products of ordinals.
Year of Submission
2014
Degree Name
Master of Arts
Department
Department of Mathematics
First Advisor
Adrienne Stanley
Date Original
2014
Object Description
1 PDF file (v, 18 pages)
Copyright
©2014 Duncan Wright
Language
en
File Format
application/pdf
Recommended Citation
Wright, Duncan, "D-spaces in infinite products of ordinals" (2014). Dissertations and Theses @ UNI. 42.
https://scholarworks.uni.edu/etd/42
