Abstract
Which Isbell-Mrówka spaces (Ψ-spaces) satisfy the star version of Menger's and Hurewicz's covering properties? Following Bonanzinga and Matveev, this question is considered here from a combinatorial point of view. An example of a Ψ-space that is (strongly) star-Menger but not star-Hurewicz is obtained. The PCF-theory function κcof([κ]ℵ0) is a key tool. Using the method of forcing, a complete answer to a question of Bonanzinga and Matveev is provided.The results also apply to the mentioned covering properties in the realm of Pixley-Roy spaces, to the extent of spaces with these properties, and to the character of free abelian topological groups over hemicompact k spaces.
| Original language | English |
|---|---|
| Pages (from-to) | 198-207 |
| Number of pages | 10 |
| Journal | Topology and its Applications |
| Volume | 192 |
| DOIs | |
| State | Published - 1 Sep 2015 |
Bibliographical note
Publisher Copyright:© 2015 Elsevier B.V.
Keywords
- Isbell-Mrówka space
- Star-Hurewicz
- Star-Menger
- Ψ-space
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