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arXiv 2005.063272020-05math.GN

On compactness and fixed point theorems in partial metric spaces

Dariusz Bugajewski, Piotr Maćkowiak, Ruidong Wang

备注：: minor corrections, 16 pages, initially submitted to a journal on November 6, 2019
发表信息：: Fixed Point Theory, Volume 23, No. 1, 2022, 163-178, February 1st, 2022
DOI：: 10.24193/fpt-ro.2022.1.10

英文摘要：

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.

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