Nhu, Nguyen ThoRodríguez Sanjurjo, José ManuelVan An, Tran2023-06-202023-06-201997-100002-993910.1090/S0002-9939-97-04020-3https://hdl.handle.net/20.500.14352/57661We 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.engjournal articlehttp://www.ams.org/journals/proc/1997-125-10/S0002-9939-97-04020-3/S0002-9939-97-04020-3.pdfhttp://www.ams.org/restricted access514515.1Convex setlinear metric spaceextreme pointabsolute retractGeometríaTopología1204 Geometría1210 Topología