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Title

Lindelöf property and the iterated continuous function spaces

Authors 1

Affiliations

  1. Faculty of Mechanics and Mathematics, Tomsk State University, Pr. Lenina 36, 634010 Tomsk, Russia

Abstract

We give an example of a compact space X whose iterated continuous function spaces Cp(X), CpCp(X),... are Lindelöf, but X is not a Corson compactum. This solves a problem of Gul'ko (Problem 1052 in [11]). We also provide a theorem concerning the Lindelöf property in the function spaces Cp(X) on compact scattered spaces with the ω1th derived set empty, improving some earlier results of Pol [12] in this direction.

Bibliography

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  12. R. Pol, Concerning function spaces on separable compact spaces, Bull. Acad. Polon. Sci. 25 (1977), 993-997.
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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm143/fm14317.pdf

Fundamenta Mathematicae
1993/143/1
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Pages:
87-95
Main language of publication
English
Received
1992-12-16
Published
1993
Exact and natural sciences