Weak-invariant properties of the norm topology-Reference-Cited by-同舟云学术

Weak-invariant properties of the norm topology

Published:1993 Issue:2 Volume:118 Page:507-511
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Namioka I.,Pol R.

Abstract

A property (P) relative to the norm topology of a Banach space is a weak-invariant if, whenever A A and B B are weakly homeomorphic subsets of (possibly different) Banach spaces and ( A A , norm) has property (P), then ( B B , norm) has property (P). We show that the property of being σ \sigma -discrete and the property of being an absolute Souslin- F \mathcal {F} space of weight ⩽ ℵ 1 \leqslant {\aleph _1} , both relative to the norm topology, are weak-invariants. These conclusions are obtained from a result concerning maps of metrizable spaces into function spaces.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1993-118-02/S0002-9939-1993-1132419-4/S0002-9939-1993-1132419-4.pdf

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