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Spaces related to \(\gamma\)-sets. (English) Zbl 1140.54005

Two theorems on \(\;k\)-\(\gamma\)-sets and \(\gamma'_k\)-sets which are closely related to the \(\gamma\)-spaces of J. Gerlits and Zs. Nagy [Topology Appl. 14, 151–161 (1982; Zbl 0503.54020)] are proved. These sets were introduced in the literature by means of selection principles and have been characterized by topological games. In this paper the corresponding characterizations are given using Ramsey theory.

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
05C55 Generalized Ramsey theory
03E02 Partition relations
91A44 Games involving topology, set theory, or logic

Citations:

Zbl 0503.54020
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