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The AR-property for Roberts’ example of a compact convex set with no extreme points Part 2: Application to the example

Authors: Nguyen To Nhu, Jose M. R. Sanjurjo and Tran Van An
Journal: Proc. Amer. Math. Soc. 125 (1997), 3089-3098
MSC (1991): Primary 54C55; Secondary 54D45
MathSciNet review: 1415358
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Abstract: In this second part of our paper, we apply the result of Part 1 to show that the compact convex set with no extreme points, constructed by Roberts (1977), is an AR.

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Nguyen To Nhu
Affiliation: Institute of Mathematics, P.O. Box 631, Bo Ho, Hanoi, Vietnam
Address at time of publication: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-8001

Jose M. R. Sanjurjo
Affiliation: Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad Complutense de Madrid, 280 40 Madrid, Spain

Tran Van An
Affiliation: Department of Mathematics, University of Vinh, Nghe An, Vietnam

Keywords: Convex set, linear metric space, extreme point, absolute retract
Received by editor(s): December 17, 1992
Received by editor(s) in revised form: April 1, 1996
Additional Notes: The first author was supported by the Complutense University of Madrid.
Communicated by: James West
Article copyright: © Copyright 1997 American Mathematical Society