The AR-property in linear metric spaces

✍ Scribed by Mohamed A. Khamsi; Nhu Nguyen; Luis Valdez-Sanchez

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 139 KB
• Volume: 109
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00179-0

✦ Synopsis

Roberts constructed a linear metric space which contains a compact convex set without any extreme points. The space constructed by Roberts is complicated and special.

We investigate the topological property of Roberts' example and demonstrate that the linear metric space constructed by Roberts is an AR, therefore is homeomorphic to Hilbert space.