Displaying similar documents to “A new approach to function spaces on quasi-metric spaces.”

On linear operators and functors extending pseudometrics

C. Bessaga (1993)

Fundamenta Mathematicae

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For some pairs (X,A), where X is a metrizable topological space and A its closed subset, continuous, linear (i.e., additive and positive-homogeneous) operators extending metrics for A to metrics for X are constructed. They are defined by explicit analytic formulas, and also regarded as functors between certain categories. An essential role is played by "squeezed cones" related to the classical cone construction. The main result: if A is a nondegenerate absolute neighborhood retract for...

Pairwise monotonically normal spaces

Josefa Marín, Salvador Romaguera (1991)

Commentationes Mathematicae Universitatis Carolinae

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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. ...