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

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, τ^b) is pairwise M₁. Here, τ:= {U Î τ |U is an upper set} and T^b:= {L Î τ |L is a lower set}.