On topological tomography of convexity
by
Evgeny Shchepin
Steklov Math. Institute
Coauthors: Luis Montejano (UNAM, Mexico)

The main result is the following theorem:

Theorem. Let B be a closed in a weak topology subset of a linear locally convex space, such that B is acyclic and all sections of B by hyperplanes are also acyclic (with respect to some exact homology theory) then B is convex.

For compact sets in finite-dimensional linear spaces and mod-2 homologies this theorem was proved by G.Aumann (see [1])

References.

[1] L.Montejano and E.Shchepin Ä characterization of convex sets in terms of acyclic support sets" Bull. London Math. Soc.28 (1996) 501-504

Date received: February 1, 2000