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Toward a topological classification of convex sets in infinite-dimensional Fréchet spaces

✍ Scribed by Taras Banakh

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 223 KB
Volume: 111
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(99)00218-7

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✦ Synopsis

Main Theorem: Let C be an infinite-dimensional convex set in a Fréchet space. If C has an almost internal point, then for every compact subset K of the completion

Ten corollaries are derived from this theorem. Among them there are (1) conditions under which two convex sets with almost internal points are homeomorphic, (2) conditions under which a convex set with an almost internal point is homeomorphic to a convex set in l 2 , (3) a characterization of convex sets with almost internal points, homeomorphic to Σ, (4) a characterization of ∞-convex sets homeomorphic to Σ ω .

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