Erweiterungen topologischer Räume
type: Item
instance of: scholarly article
title: Erweiterungen topologischer Räume
zbMATH Open document ID: 0569.54026
DOI: 10.1007/BF01299271
author: Gerhard Wilke
published in: Monatshefte für Mathematik
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178252
review text: An extension principle for \(T_ 0\)-spaces is formulated which includes several well-known compactifications. As an application we get, e.g., the following: For any non-empty, open subset \(D\subseteq {\mathbb{R}}^ n\), the ring of all \(C^{\infty}\)-functions on D satisfies the pm-condition (i.e., every prime ideal is contained in a unique maximal ideal) and induces a Stone-Čech compactification of D. Finally, it is shown that the compact \(T_ 2\)-spaces are exactly the \(T_ 1\)-retracts of Stone spaces, and the \(T_ 2\)-compactifications of a given space are characterized similarly. All these results are derived from some general facts on semirings stated in the first part of the paper.
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54C40
Mathematics Subject Classification ID: 26E10
zbMATH DE Number: 3909309
zbMATH Keywords: extension principle
zbMATH Keywords: ring of all \(C^{\infty }\)-functions
zbMATH Keywords: pm-condition
zbMATH Keywords: \(T_ 1\)-retracts of Stone spaces
zbMATH Keywords: \(T_ 2\)-compactifications
zbMATH Keywords: semirings
MaRDI profile type: Publication
cites work: Wallman-Type Compactifications
cites work: On pm-rings
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description: scientific article; zbMATH DE number 3909309