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Le degré de Lindelöf est $l$-invariant

Author: Ahmed Bouziad
Journal: Proc. Amer. Math. Soc. 129 (2001), 913-919
MSC (2000): Primary 54C35; Secondary 46E10
Published electronically: 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

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
Published electronically: September 19, 2000
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society

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