DMS Set Theoretic Topology Seminar

Speaker: Mike Reed, St Edmund Hall, Oxford University

Title: Open Questions Concerning Compactness Conditions in Moore Spaces

Abstract: All spaces are considered to be regular and T_1.

Definition. A space S is 1-starcompact if for each open covering U of S, there exists a finite subcollection V of U such that each member of U has non-empty intersection with a member of V.

Questions.

1. In  ZFC, is each 1-starcompact Moore space compact?

2. In ZFC, does there exist a first countable, 1-starcompact space that is not countable compact?

3. In ZFC, is each normal, separable Moore space Scott-representable?

4. In ZFC, does there exist a cwH Moore space that is not cwn with respect to compact sets?

5. Is there a consistent with ZFC example of a normal, locally compact, separable Moore space S such that the square of S is not normal?

The speaker presents construction techniques relevant to these open questions.