On decompositions of compact convex sets

by    C. Richter

Preprint series: 99-35, Reports on Algebra and Geometry

The paper is published: Geom. Dedicata 71 (1998), 1-4

MSC:
52A07 Convex sets in topological vector spaces, See also {46A55}
52A55 Spherical and hyperbolic convexity
52A01 Axiomatic and generalized convexity

Abstract: The present paper generalizes M. Edelstein's theorem on the
indecomposability of compact convex sets in locally convex
linear topological spaces to spherical and hyperbolic
geometry. Moreover, the indecomposability of compact
intervals in $E^1$ w.r.t. homeomorphisms of $E^1$ onto
itself is shown.

Keywords: indecomposability of compact convex sets, spherical and hyperbolic convexity, affine isomorphism, isometry

Upload: 1999-07-26


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