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The AR-property for Roberts' example of a compact convex set with no extreme points .1. General result

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Nhu, Nguyen Tho and Rodríguez Sanjurjo, José Manuel and Van An, Tran (1997) The AR-property for Roberts' example of a compact convex set with no extreme points .1. General result. Proceedings of the American Mathematical Society, 125 (10). pp. 3075-3087. ISSN 0002-9939

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Official URL: http://www.ams.org/journals/proc/1997-125-10/S0002-9939-97-04020-3/S0002-9939-97-04020-3.pdf


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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.


Item Type:Article
Uncontrolled Keywords:Convex set, linear metric space, extreme point, absolute retract
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:16901
Deposited On:26 Oct 2012 10:31
Last Modified:12 Dec 2018 15:13

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