Endomorphisms of homogeneous spaces of Lie groups (Q1804710)

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 \((G/H)^H\).