On the reconstruction of locally convex spaces from their groups of homeomorphisms Academic Article uri icon


  • Abstract 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 ϕ between H (X) and H (Y), then there exists a homeomorphism π between X and Y such that for every h∈ H (X), ϕ (h)= π◦ h◦ π− 1.

publication date

  • January 1, 1999