Some remarks and examples on interpolative metric spaces
DOI:
https://doi.org/10.66147/lnaa.20264284Keywords:
Interpolative metric space, b-metric space, quasi-normed spaceAbstract
In an article published in 2024, the first named author introduced the concept of an interpolative metric space. These spaces constitute an appealing subclass of the class of $b$-metric spaces. Indeed, we recently stated that, in contrast to the $b$-metric case, any interpolative metric is a continuous function and "open" balls are open sets in the induced topology. In this note, we also observe that for any interpolative metric space, "closed" balls are closed sets in the induced topology, and show that some essential quasi-normed spaces can be structured as interpolative metric spaces.
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Copyright (c) 2026 Erdal Karapınar (Corresponding Author); Salvador Romaguera
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