The AR-property for Roberts' example

of a compact convex set with no extreme points

Part 1: general result

Authors:
Nguyen To Nhu, Jose M. R. Sanjurjo and Tran Van An

Journal:
Proc. Amer. Math. Soc. **125** (1997), 3075-3087

MSC (1991):
Primary 54C55; Secondary 54D45

DOI:
https://doi.org/10.1090/S0002-9939-97-04020-3

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the original compact convex set with no extreme points, constructed by Roberts (1977) is an absolute retract, therefore is homeomorphic to the Hilbert cube. Our proof consists of two parts. In this first part, we give a sufficient condition for a Roberts space to be an AR. In the second part of the paper, we shall apply this to show that the example of Roberts is an AR.

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Additional Information

**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

Email:
nnguyen@nmsu.edu

**Jose M. R. Sanjurjo**

Affiliation:
Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad Complutense de Madrid, 280 40 Madrid, Spain

Email:
sanjurjo@sungt1.mat.ucm.es

**Tran Van An**

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

DOI:
https://doi.org/10.1090/S0002-9939-97-04020-3

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