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Journal of the London Mathematical Society 1997 56(3):584-594; doi:10.1112/S0024610797005504
© 1997 by London Mathematical Society
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© The London Mathematical Society

The Finite Dimensional Approximation Property and the AR-Property in Needle Point Spaces

Nguyen To Nhu

Institute of Mathematics P.O. Box 631, Bo Ho, Hanoi, Vietnam

Received 7 February 1994. Revision received 12 December 1995.

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.

Department of Mathematical Science, The University of Texas at El Paso El Paso, Texas 79968, USA. E-mail address: nguyen{at}math.utep.edu


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