Currently displaying 1 – 1 of 1

Showing per page

Order by Relevance | Title | Year of publication

Topological games and product spaces

Salvador García-FerreiraR. A. González-SilvaArtur Hideyuki Tomita — 2002

Commentationes Mathematicae Universitatis Carolinae

In this paper, we deal with the product of spaces which are either 𝒢 -spaces or 𝒢 p -spaces, for some p ω * . These spaces are defined in terms of a two-person infinite game over a topological space. All countably compact spaces are 𝒢 -spaces, and every 𝒢 p -space is a 𝒢 -space, for every p ω * . We prove that if { X μ : μ < ω 1 } is a set of spaces whose product X = μ < ω 1 X μ is a 𝒢 -space, then there is A [ ω 1 ] ω such that X μ is countably compact for every μ ω 1 A . As a consequence, X ω 1 is a 𝒢 -space iff X ω 1 is countably compact, and if X 2 𝔠 is a 𝒢 -space, then all...

Page 1

Download Results (CSV)