Separation axioms for interval topologies
- authored by
- 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.
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
- Type
- Article
- Journal
- Proceedings of the American Mathematical Society
- Volume
- 79
- Pages
- 185-190
- No. of pages
- 6
- ISSN
- 0002-9939
- Publication date
- 06.1980
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- General Mathematics, Applied Mathematics
- Electronic version(s)
-
https://doi.org/10.1090/S0002-9939-1980-0565335-8 (Access:
Open)
