Abstract: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.
Keywords: pairwise monotonically normal space, quasi-metrizable bitopological space, pairwise stratifiable space, pairwise compact space
AMS Subject Classification: 54E55, 54D15, 54C30, 54E35, 54E20