Metrics and Quasimetrics Induced by Point Pair Function
Rainio Oona; Vuorinen Matti; Dautova Dina; Nasyrov Semen
Metrics and Quasimetrics Induced by Point Pair Function
Rainio Oona
Vuorinen Matti
Dautova Dina
Nasyrov Semen
SPRINGER HEIDELBERG
Julkaisun pysyvä osoite on:
https://urn.fi/URN:NBN:fi-fe2022091258767
https://urn.fi/URN:NBN:fi-fe2022091258767
Tiivistelmä
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.
Kokoelmat
- Rinnakkaistallenteet [19207]