On the reconstruction of Boolean algebras from their automorphism groups.
The theory of boolean algebras with a distinguished subalgebra is undecidable
Reconstruction of manifolds and subsets of normed spaces from subgroups of their homeomorphism groups
This work concerns topological spaces of the following types: open subsets of normed vector spaces, manifolds over normed vector spaces, the closures of open subsets of normed vector spaces and some other types of topological spaces related to the above. We show that such spaces are determined by various subgroups of their auto-homeomorphism groups. Theorems 1-3 below are typical examples of the results obtained in this work. Theorem 1. For a metric space X let UC(X) denote the group of all auto-homeomorphisms...
Extension and reconstruction theorems for the Urysohn universal metric space
We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. As an application, we prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.
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