TY - JOUR
T1 - On M1- and M3-properties in the setting of ordered topological spaces
AU - Künzi, Hans Peter A.
AU - Mushaandja, Zechariah
N1 - Publisher Copyright:
© 2015, Hacettepe Journal of Mathematics and Statistics. All rights reserved.
PY - 2015
Y1 - 2015
N2 - 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}.
AB - 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}.
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U2 - 10.15672/HJMS.2015449680
DO - 10.15672/HJMS.2015449680
M3 - Article
AN - SCOPUS:84961647349
SN - 1303-5010
VL - 44
SP - 1391
EP - 1395
JO - Hacettepe Journal of Mathematics and Statistics
JF - Hacettepe Journal of Mathematics and Statistics
IS - 6
ER -