Open Access Thesis
Numbers; Ordinal; Covering spaces (Topology);
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
Master of Arts
Department of Mathematics
1 PDF file (v, 18 pages)
2014 - Duncan Wright
Wright, Duncan, "D-spaces in infinite products of ordinals" (2014). Electronic Theses and Dissertations. 42.