Partial Metric Spaces

The topic of this section has its origins in the study of theoretical computer science. In 1992, S.G. Matthews [149] introduced the notion of a “partial metric space” with the aim of providing a quantitative mathematical model suitable for programming verification. See [149, 200] for further discussion. Among other things, Matthews proved a partial metric version of the celebrated Banach fixed point theorem which has become an appropriate quantitative fixed point technique to capture the meaning of recursive denotational specifications in programming languages.