DOI: 10.24193/fpt-ro.2022.1.10

Authors: Dariusz Bugajewski, Piotr Maćkowiak and Ruidong Wang

Abstract: In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that Hausdorff compact partial metric spaces are metrizable. In the second part of this article we discuss the significance of bottom sets of partial metric spaces in fixed point theorems for mappings acting in these spaces.

Key Words and Phrases: Banach Contraction Principle, compactness, completeness, fixed point theorem, metrizability, partial metric spaces, sequential compactness.

2010 Mathematics Subject Classification: 54D30, 54E35, 54E50, 54H25.

Published on-line: February 1st, 2022.

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