Title of article
On a theorem of Grothendieck in Cp-theory
Author/Authors
Arhangelʹskii، نويسنده , , A.V.، نويسنده ,
Issue Information
دوماهنامه با شماره پیاپی سال 1997
Pages
21
From page
21
To page
41
Abstract
A theorem of Grothendieck is extended in several directions. In particular, it is proved that if X is a Lindelöf ∑-space, then the closure of every relatively countably compact subset of Cp(X) is compact. We also investigate when the closure of every pseudocompact subspace of Cp(X) is compact, and when every pseudocompact subset of Cp(X) is itself compact, or even belongs to a given class of compacta. New open questions are formulated.
Keywords
Lindelِf spaces , Eberlein compactum , pointwise convergence , Fréchet-Urysohn space , Function space , Corson compactum , Countable tightness
Journal title
Topology and its Applications
Serial Year
1997
Journal title
Topology and its Applications
Record number
1575721
Link To Document