Article ID Journal Published Year Pages File Type
4657740 Topology and its Applications 2017 10 Pages PDF
Abstract

Topological properties of quotients of topological groups with respect to compact subgroups are investigated. It is observed that many classical results on topological groups can be extended to coset spaces of this kind. The main results of the paper are presented in the last sections. Among them is the Dichotomy Theorem for coset spaces with respect to a compact subgroup which says that every remainder of any such coset space is either pseudocompact or metric-friendly. Several metrizability conditions for coset spaces in terms of their remainders are given.

Related Topics
Physical Sciences and Engineering Mathematics Geometry and Topology
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