DAS WALLMAN-VERFAHREN UND INVERSE LIMITES

1 January 1977

journal article
Published by Taylor & Francis in Quaestiones Mathematicae

Vol. 2 (1-3) , 325-333
https://doi.org/10.1080/16073606.1977.9632552

Abstract

The relationship between Wallman's construction of a compact T₁-space [9] and Flachsmeyer's inverse limit spaces of inverse systems of decomposition spaces [2] is investigated. There are connections between Wallman spaces and inverse limits, which were initiated by Alexandroff in 1928. Some old theorems using inverse limits have shorter proofs now. On the other hand we obtain a new method to treat Wallman compactifications in terms of inverse limit spaces. A suitable notion in this context is the “prime-filter space”, having an interesting maximality property. This space seems to be proper to examine prime ideals in C(X).

Keywords

This publication has 7 references indexed in Scilit:

Allgemeine Topologie
Published by Springer Nature ,1972
On Wallman compactifications
Fundamenta Mathematicae, 1967
Wallman spaces and compactifications
Fundamenta Mathematicae, 1967
Compactifications and Semi-Normal Spaces
American Journal of Mathematics, 1964
Zur Spektralentwicklung topologischer Räume
Mathematische Annalen, 1961
Rings of Continuous Functions
Published by Springer Nature ,1960
Lattices and Topological Spaces
Annals of Mathematics, 1938