Laitinen, Erkki Endomorphisms of homogeneous spaces of Lie groups. (English) Zbl 0829.22011 Osaka J. Math. 32, No. 1, 165-170 (1995). 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 Keywords:structure of homogeneous spaces PDFBibTeX XMLCite \textit{E. Laitinen}, Osaka J. Math. 32, No. 1, 165--170 (1995; Zbl 0829.22011)