## The AR-property for Roberts’ example of a compact convex set with no extreme points Part 1: General result

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- by Nguyen To Nhu, Jose M. R. Sanjurjo and Tran Van An
- Proc. Amer. Math. Soc.
**125**(1997), 3075-3087 - DOI: https://doi.org/10.1090/S0002-9939-97-04020-3
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## 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.## References

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## Bibliographic 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
- 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
- © Copyright 1997 American Mathematical Society
- 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
- MathSciNet review: 1415357