Lindelöf Degree and Function Spaces

Vesko Valov () and Dumisani Vuma ()
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Vesko Valov: University of Swaziland, Department of Mathematics
Dumisani Vuma: University of Zimbabwe, Department of Mathematics

A chapter in Papers in Honour of Bernhard Banaschewski, 2000, pp 475-483 from Springer

Abstract: Abstract We prove that if X and Y are completely regular perfect spaces and Φ is a continuous linear homeomorphism between C p (X) and C p (Y) (resp., C p * (X) and C p * (Y)) then the Lindelöf degrees of X and Y are the same. When Φ is positive the above result remains true for any completely regular X and Y. It is also shown that pseudocompactness and compactness are preserved by continuous linear homeomorphisms between C p * (X) and C p * (Y).

Keywords: 54C35; 57N17; function spaces; Lindelöf degree; linear homeomorphism. (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-2529-3_29

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DOI: 10.1007/978-94-017-2529-3_29

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