On the Reconstruction of locally convex spaces from their groups of homeomorphisms by A. Leiderman and M. Rubin

Electronic Version 24 Summer (1999)

On the Reconstruction of locally convex spaces from their groups of homeomorphisms

A. Leiderman and M. Rubin

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^-1.

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Topology Proceedings Electronic Version