Electronic Theses and Dissertations

Author

Duncan Wright

Award/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.

Date of Award

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)

Language

EN

File Format

application/pdf

Included in

Mathematics Commons

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