On M1- and M3-properties in the setting of ordered topological spaces

Hans Peter A. Künzi, Zechariah Mushaandja

Research output: Contribution to journalArticle

Abstract

In 1961, J. G. Ceder [3] introduced and studied classes of topological spaces called Mi-spaces (i = 1; 2; 3) and established that metrizable ÞM1 Þ M2 Þ M3. He then asked whether these implications are reversible. Gruenhage [5] and Junnila [8] independently showed that M3 Þ M2. In this paper, we investigate the M1- and M3- properties in the setting of ordered topological spaces. Among other results, we show that if (X, T, ≤) is an M1 ordered topological C- and I-space then the bitopological space (X, τ, τb) is pairwise M1. Here, τ:= {U Î τ |U is an upper set} and Tb:= {L Î τ |L is a lower set}.

Original languageEnglish
Pages (from-to)1391-1395
Number of pages5
JournalHacettepe Journal of Mathematics and Statistics
Volume44
Issue number6
DOIs
Publication statusPublished - Jan 1 2015

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Topological space
Bitopological Space
Metrizable
Pairwise
Class

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Statistics and Probability
  • Geometry and Topology

Cite this

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abstract = "In 1961, J. G. Ceder [3] introduced and studied classes of topological spaces called Mi-spaces (i = 1; 2; 3) and established that metrizable {\TH}M1 {\TH} M2 {\TH} M3. He then asked whether these implications are reversible. Gruenhage [5] and Junnila [8] independently showed that M3 {\TH} M2. In this paper, we investigate the M1- and M3- properties in the setting of ordered topological spaces. Among other results, we show that if (X, T, ≤) is an M1 ordered topological C- and I-space then the bitopological space (X, τ, τb) is pairwise M1. Here, τ:= {U {\^I} τ |U is an upper set} and Tb:= {L {\^I} τ |L is a lower set}.",
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On M1- and M3-properties in the setting of ordered topological spaces. / Künzi, Hans Peter A.; Mushaandja, Zechariah.

In: Hacettepe Journal of Mathematics and Statistics, Vol. 44, No. 6, 01.01.2015, p. 1391-1395.

Research output: Contribution to journalArticle

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