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

Nhu, Nguyen; Sanjurjo, Jose; An, Tran

doi:10.1090/S0002-9939-97-04020-3

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.

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