Extending of partial metrics

Authors

  • V. Mykhaylyuk Yuriy Fedkovych Chernivtsi National University, 2 Kotsyubynskyi str., 58012, Chernivtsi, Ukraine; Jan Kochanowski University of Kielce, 5 Żeromskiego str., 25369, Kielce, Poland https://orcid.org/0000-0002-6675-3182
  • V. Myronyk Yuriy Fedkovych Chernivtsi National University, 2 Kotsyubynskyi str., 58012, Chernivtsi, Ukraine
https://doi.org/10.15330/cmp.17.1.33-41

Keywords:

partial metric, quasi-metric, partially metrizable space, metrizable space, extension of metric, extension of quasi-metric, extension of partial metric, topological space
Published online: 2025-01-31

Abstract

We investigate the following question: does there exist a compatible extension of a given compatible partial metric p:A2→R on a closed subset A of a partially metrizable space X? We obtain a positive answer to this question in the case when the corresponding quasi-metric qp(x,y)=p(x,y)−p(x,x) has an extension that generates a weaker topology on X (in particular, if qp is bounded). Moreover, we give an example which shows that in general the answer to the question is negative.

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How to Cite
(1)
Mykhaylyuk, V.; Myronyk, V. Extending of Partial Metrics. Carpathian Math. Publ. 2025, 17, 33-41.