Abstract
Whereas the Gerlits-Nagy γ property is strictly weaker than the Galvin-Miller strong γ property, the corresponding strong notions for the Menger, Hurewicz, Rothberger, Gerlits-Nagy (*), Arkhangel'skiǐ and Sakai properties are equivalent to the original ones. The main result is that almost each of these properties admits the game theoretic characterization suggested by the stronger notion. We also solve a related problem of Kočinac and Scheepers, and answer a question of Iliadis.
| Original language | English |
|---|---|
| Pages (from-to) | 620-639 |
| Number of pages | 20 |
| Journal | Topology and its Applications |
| Volume | 153 |
| Issue number | 4 |
| DOIs | |
| State | Published - 1 Nov 2005 |
| Externally published | Yes |
Keywords
- Arkhangel'skiǐ property
- Galvin-Miller strong γ property
- Gerlits-Nagy (*) property
- Gerlits-Nagy γ property
- Hurewicz property
- Infinite game theory
- Menger property
- Rothberger property
- Sakai property
- Selection principles