Separation axioms for interval topologies

verfasst von

Marcel ErnÉ

Abstract

In Theorem 1 of this note, results of Kogan [2], Kolibiar [3], Matsushima [4] and Wölk [7] concerning interval topologies are presented under a common point of view, and further characterizations of the T₂ axiom are obtained. A sufficient order-theoretical condition for regularity of interval topologies is established in Theorem 2. In lattices, this condition turns out to be equivalent both to the T₂ and to the T₃ axiom. Hence, a Hausdorf f interval topology of a lattice is already regular. However, an example of a poset is given where the interval topology is T₂ but not T₃.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Artikel

Journal

Proceedings of the American Mathematical Society

Band

79

Seiten

185-190

Anzahl der Seiten

6

ISSN

0002-9939

Publikationsdatum

06.1980

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Allgemeine Mathematik, Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.1090/S0002-9939-1980-0565335-8 (Zugang: Offen)