2017/10/28 by Popvassilev, Strashimir G., Porter, John E.
#54D20 #54D30 #54D65 #54E35 #54F05 #FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.1710.10374
We continue Gartside, Moody, and Stares' study of versions of monotone paracompactness. We show that the class of spaces with a monotone closure-preserving open operator is strictly larger than those with a monotone open locally-finite operator. We prove that monotonically metacompact GO-spaces have a monotone open locally-finite operator, and so do GO-spaces with a monotone (open or not) closure-preserving operator, whose underlying LOTS has a σ-closed-discrete dense subset. A GO-space with a σ-closed-discrete dense subset and a monotone closure-preserving operator is metrizable. A compact LOTS with a monotone open closure-preserving operator is metrizable.