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Countably compact first countable subspaces of ordinals have the Sokolov property.
- Source :
- QM - Quaestiones Mathematicae; Jun2011, Vol. 34 Issue 2, p225-234, 10p
- Publication Year :
- 2011
-
Abstract
- A space X is Sokolov if for any sequence {Fn : n ∈ } where Fn is a closed subset of Xn for every n ∈ , there exists a continuous map f : X → X such that nw(f(X)) ≤ ω and fn(Fn) ⊂ Fn for all n ∈ . We prove that if X is a first countable countably compact subspace of an ordinal then X is a Sokolov space and CP(X) is a D-space; this answers a question of Buzyakova. Thus, for any first countable countably compact subspace X of an ordinal, the iterated function space Cp, 2n+1(X) is Lindelof for any n ∈ ω Another consequence of the above results is the existence of a first countable Sokolov space of cardinality greater than c. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16073606
- Volume :
- 34
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- QM - Quaestiones Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 63295736
- Full Text :
- https://doi.org/10.2989/16073606.2011.594237