Quantitative continuous Δ-spaces

Abstract

Partial metric spaces are a generalization of the usual metric spaces in which self-distance need not be zero; they play an important role in the study of non-Hausdorff topologies. In this paper, for so-called Δ-spaces (which are typically non-Hausdorff ), we introduce the notions of Δ-basis and algebraicity, and we give several characterizations of the latter notion. Furthermore, we prove that every ω-continuous Δ-space is partially metrizable.