Metrics and Quasimetrics Induced by Point Pair Function

: Dautova Dina, Nasyrov Semen, Rainio Oona, Vuorinen Matti

Publisher: SPRINGER HEIDELBERG

: 2022

: Boletim da Sociedade Brasileira de Matemática / Bulletin of the Brazilian Mathematical Society

: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY

: B BRAZ MATH SOC

: 25

: 1678-7544

: 1678-7714

DOI: https://doi.org/10.1007/s00574-022-00309-5

: https://link.springer.com/article/10.1007/s00574-022-00309-5

: 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.

s00574-022-00309-5.pdf