A universal topological group with a countable base
Copyright policy )A universal topological group with a countable base
If \(Q\) is the Hilbert cube and \(\Aut Q\) is the group of all homeomorphisms from \(Q\) to itself with the compact-open topology then the author proves the following theorem: Any topological group with countable basis is topologically isomorphic to some subgroup of the group \(\Aut Q\). The consequence is that there exists a separable Banach space \(E\) such that any topological group with countable basis is isomorphic to some subgroup of the group of all linear isometries on \(E\). It holds for \(E=C(Q)\).
separable Banach space, universal topological group, Structure of general topological groups, Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product), Hilbert cube, countable basis
separable Banach space, universal topological group, Structure of general topological groups, Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product), Hilbert cube, countable basis
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