Fibrations and coset spaces for locally compact groups

TL;DR

This paper proves that for a topological group with certain subgroup conditions, the quotient map is a fibration, extending known results and providing new insights into the structure of locally compact groups.

Contribution

It establishes that the quotient map from G/K to G/L is a fibration when L is a locally compact pro-Lie group, generalizing previous results.

Findings

The map q:G/K to G/L is a fibration under specified conditions.

Extension of classical results by Skljarenko, Madison, and Mostert.

Provides new tools for analyzing the topology of quotient spaces.

Abstract

Let $G$ be a topological group and let $K,L\subseteq G$ be closed subgroups, with $K\subseteq L$. We prove that if $L$ is a locally compact pro-Lie group, then the map $q:G/K\to G/L$ is a fibration. As an application of this, we obtain two older results by Skljarenko, Madison and Mostert.