Fibrations and Coset Spaces for Locally Compact Groups

Let G be a topological group and let K,L subset of G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K,L\subseteq G$$\end{document} be closed subgroups, with K subset of L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K\subseteq L$$\end{document}. We prove that if L is a locally compact pro-Lie group, then the map q:G/K -> G/L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q:G/K\rightarrow G/L$$\end{document} is a Serre fibration, and a Hurewicz fibration if G is paracompact. As an application of this, we obtain two older results by Skljarenko, Madison and Mostert.