A1 Refereed original research article in a scientific journal
Metrics and Quasimetrics Induced by Point Pair Function
Authors: Dautova Dina, Nasyrov Semen, Rainio Oona, Vuorinen Matti
Publisher: SPRINGER HEIDELBERG
Publication year: 2022
Journal: Boletim da Sociedade Brasileira de Matemática / Bulletin of the Brazilian Mathematical Society
Journal name in source: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY
Journal acronym: B BRAZ MATH SOC
Number of pages: 25
ISSN: 1678-7544
eISSN: 1678-7714
DOI: https://doi.org/10.1007/s00574-022-00309-5
Web address : https://link.springer.com/article/10.1007/s00574-022-00309-5
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/176154861
We study the point pair function in subdomains G of R-n. We prove that, for every domain G subset of R-n, this function is a quasi-metric with the constant less than or equal to root 5/2. Moreover, we show that it is a metric in the domain G = R-n\{0} with n >= 1. We also consider generalized versions of the point pair function, depending on a parameter alpha > 0, and show that in some domains these generalizations are metrics if and only if alpha <= 12.
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