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THE FINITE DIMENSIONAL APPROXIMATION PROPERTY AND THE AR-PROPERTY IN NEEDLE POINT SPACES

Published online by Cambridge University Press:  01 December 1997

NGUYEN TO NHU
Affiliation:
Institute of Mathematics, P.O. Box 631, Bo Ho, Hanoi, Vietnam Current address: Department of Mathematical Science, The University of Texas at El Paso, El Paso, Texas 79968, USA. E-mail address: nguyen@math.utep.edu
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Abstract

We introduce the notion of the finite dimensional approximation property (the FDAP) and prove that if a subset X of a linear metric space has the FDAP, then every non-empty convex subset of X is an AR.

As an application we show that every needle point space X contains a dense linear subspace E with the following properties:

(i) E contains a non-empty compact convex set with no extreme points;

(ii) all non-empty convex subsets of E are AR.

Type
Notes and Papers
Copyright
The London Mathematical Society 1997

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