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Open mappings of locally compact groups

Michael G. Cowling, Karl H. Hofmann, Sidney A. Morris

Abstract

The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.

Open mappings of locally compact groups

Abstract

The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.
Paper Structure (3 sections, 6 theorems, 5 equations)

This paper contains 3 sections, 6 theorems, 5 equations.

Table of Contents

  1. Main result
  2. Another version
  3. Comments

Key Result

Theorem 2

Let $\phi\colon G\to H$ be a morphism of locally compact groups. If $\phi(G_1)$ is open in $H$ for all $G_1$ in $\mathcal{O}(G)$, then $\phi$ is an open mapping.

Theorems & Definitions (12)

  • Theorem 2
  • Remark 3
  • proof
  • Corollary 4
  • proof
  • Corollary 5
  • proof
  • Lemma 6
  • proof
  • Corollary 7
  • ...and 2 more