Strong γ-sets and other singular spaces

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11 Scopus citations


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 languageEnglish
Pages (from-to)620-639
Number of pages20
JournalTopology and its Applications
Issue number4
StatePublished - 1 Nov 2005
Externally publishedYes


  • 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


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