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 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Le degré de Lindelöf est $l$-invariant

Author(s): Ahmed Bouziad
Journal: Proc. Amer. Math. Soc. 129 (2001), 913-919.
MSC (2000): Primary 54C35; Secondary 46E10
Posted: September 19, 2000
MathSciNet review: 1707509
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Abstract: Two Tychonoff spaces $X$ and $Y$ are said to be $l$-equivalent if $C_{p}(X)$ and $C_{p}(Y)$ are linearly homeomorphic. It is shown that if $X$ and $Y$ are $l$-equivalent, then the Lindelöf numbers of $X$ and $Y$ are the same. The proof given is a strengthening of the one given by N.V. Velichko to show that the Lindelöf property is $l$-invariant.

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Additional Information:

Ahmed Bouziad
Affiliation: Département de Mathématiques, Université de Rouen, CNRS UPRES-A 6085, 76821 Mont Saint-Aignan, France
Email: Ahmed.Bouziad@univ-rouen.fr

DOI: 10.1090/S0002-9939-00-05553-2
PII: S 0002-9939(00)05553-2
Keywords: Set-valued maps, Lindel\"{o}f degree, linear homeomorphism, function spaces
Received by editor(s): January 20, 1999
Received by editor(s) in revised form: May 14, 1999
Posted: September 19, 2000
Communicated by: Alan Dow
Copyright of article: Copyright 2000, American Mathematical Society




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