Harman Patil (Editor)

Polish group

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In mathematics, a Polish group is a topological group that is also a Polish space, in other words homeomorphic to a separable complete metric space.

Contents

Examples

  • All finite dimensional Lie groups with a countable number of components are Polish groups.
  • The unitary group of a separable Hilbert space (with the strong topology) is a Polish group.
  • The group of homeomorphisms of a compact metric space is a Polish group.
  • The product of a countable number of Polish groups is a Polish group.
  • The group of isometries of a separable complete metric space is a Polish group.

    • Properties

    The group of homeomorphisms of the Hilbert cube [0,1]N is a universal Polish group, in the sense that every Polish group is isomorphic to a closed subgroup of it.

    References

    Polish group Wikipedia
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