On the reconstruction of locally convex spaces from their groups of homeomorphisms
by
Arkady Leiderman
Ben-Gurion University, Beer-Sheva, Israel
Coauthors: Matatiahu Rubin (Beer-Sheva)

Let X and Y be normal locally convex spaces that have a nonempty open set which intersect every straight line in a bounded set, and let H(X), H(Y) denote the groups of self-homeomorphisms of X and Y respectively. Our main goal is to prove the following reconstruction theorem. If there is an isomorphism \phi between H(X) and H(Y), then there exists a homeomorphism \pi between X and Y such that for every h in H(X), \phi(h) = \pi o h o \pi\inverse. As a consequence, the free locally space L(K), where K is a metrizable compact, can be reconstructed from the group of homeomorphisms.

Date received: June 4, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacl-44.