Topological ordered C- (resp. I-)spaces and generalized metric spaces

Hans Peter A. Künzi, Zechariah Mushaandja

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The following result due to Hanai, Morita, and Stone is well known: Let f be a closed continuous map of a metric space X onto a topological space Y. Then the following statements are equivalent: (i) Y satisfies the first countability axiom; (ii) for each y ∈ Y, f- 1 {y} has a compact boundary in X; (iii) Y is metrizable. In this article we obtain several related results in the setting of topological ordered spaces. In particular we investigate the upper and lower topologies of metrizable topological ordered spaces which are both C- and I-spaces in the sense of Priestley.

Original languageEnglish
Pages (from-to)2914-2922
Number of pages9
JournalTopology and its Applications
Volume156
Issue number18
DOIs
Publication statusPublished - Dec 1 2009

Fingerprint

Generalized Metric Space
Ordered Space
Metrizable
Closed Map
Continuous Map
Axiom
Topological space
Metric space
Topology

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

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Topological ordered C- (resp. I-)spaces and generalized metric spaces. / Künzi, Hans Peter A.; Mushaandja, Zechariah.

In: Topology and its Applications, Vol. 156, No. 18, 01.12.2009, p. 2914-2922.

Research output: Contribution to journalArticle

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