The equicontinuous structure relation and extension of continuous equivariant functions
type: Item
instance of: scholarly article
title: The equicontinuous structure relation and extension of continuous equivariant functions
zbMATH Open document ID: 0615.54028
DOI: 10.1216/RMJ-1986-16-4-837
author: Jan de Vries
published in: Rocky Mountain Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let \(f: A\to B\) be a morphism of a category \({\mathcal K}\), then an object C of \({\mathcal K}\) is called an injective object of f if for every morphism \(g: A\to C\) there exists a morphism \(h: B\to C\) with \(g=h\cdot f\). Let G be a topological group. Every equicontinuous G-space (K,\(\alpha)\) where K is a metrizable compact convex subset of a locally convex topological vector space is an injective object of a closed equivariant embedding \(i:(A,\pi)\to (X,\pi)\) in the category of compact Hausdorff G-spaces if and only if every almost periodic function on A can be extended to an almost periodic function on X. This fact is proved using methods of topological dynamics.
Mathematics Subject Classification ID: 54H15
Mathematics Subject Classification ID: 54C20
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 3996631
zbMATH Keywords: injective object
zbMATH Keywords: equicontinuous G-space
zbMATH Keywords: category of compact Hausdorff G-spaces
zbMATH Keywords: almost periodic function
reviewed by: Václav Koubek
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3996631