Semi-Lipschitz Functions and Best Approximation in Quasi-Metric Spaces

Abstract

We show that the set of semi-Lipschitz functions, defined on a quasi-metric space (X, d), that vanish at a fixed point x0∈X can be endowed with the structure of a quasi-normed semilinear space. This provides an appropriate setting in which to characterize both the points of best approximation and the semi-Chebyshev subsets of quasi-metric spaces. We also show that this space is bicomplete. © 2000 Academic Press.