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Endomorphisms of homogeneous spaces of Lie groups. (English) Zbl 0829.22011

If \(H\) is a closed subgroup of a topological group \(G\), the bijection \(\text{Map}_G (G/H, G/H) \overset \sim {} (G/H)^H\) is a homeomorphism, when the mapping space is equipped with compact-open topology. Homeomorphisms correspond to the subspaces \(\text{Homeo}_G (G/H) \overset \sim {} NH/H\). In the paper the following theorem is proved: Theorem. If \(G\) is a Lie group and \(H\) is a closed subgroup, then \(NH/H\) is open in \((G/H)^H\).
Reviewer: K.Riives (Tartu)

MSC:

22E15 General properties and structure of real Lie groups
22E40 Discrete subgroups of Lie groups
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