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Keywords:
pairwise monotonically normal space; quasi-metrizable bitopological space; pairwise stratifiable space; pairwise compact space
pairwise monotonically normal space; quasi-metrizable bitopological space; pairwise stratifiable space; pairwise compact space
Summary:
We introduce and study the notion of pairwise monotonically normal space as a bitopological extension of the monotonically normal spaces of Heath, Lutzer and Zenor. In particular, we characterize those spaces by using a mixed condition of insertion and extension of real-valued functions. This result generalizes, at the same time improves, a well-known theorem of Heath, Lutzer and Zenor. We also obtain some solutions to the quasi-metrization problem in terms of the pairwise monotone normality.
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