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On functions preserving products of certain classes of semimetric spaces

In: Tatra Mountains Mathematical Publications, vol. 78, no. 1
Mateusz Lichman - Piotr Nowakowski - Filip Turoboś
Detaily:
Rok, strany: 2021, 175 - 198
Jazyk: eng
Kľúčové slová:
semimetrics, metric-preserving functions, $b$-metrics, subadditive functions.
Typ článku: Mathematics
Typ dokumentu: scientific paper
O článku:
In the paper, we continue the research of Borsík and Doboš on functions which allow us to introduce a metric to the product of metric spaces. We extend their scope to a broader class of spaces which usually fail to satisfy the triangle inequality, albeit they tend to satisfy some weaker form of this axiom. In particular, we examine the behavior of functions preserving $b$-metric inequality. We provide analogues of the results of Borsík and Doboš adjusted to the new broader setting. The results we obtained are illustrated with multitude of examples. Furthermore, the connections of newly introduced families of functions with the ones already known from the literature are investigated.
Ako citovať:
ISO 690:
Lichman, M., Nowakowski, P., Turoboś, F. 2021. On functions preserving products of certain classes of semimetric spaces. In Tatra Mountains Mathematical Publications, vol. 78, no.1, pp. 175-198. 1210-3195. DOI: https://doi.org/ 10.2478/tmmp-2021-0013

APA:
Lichman, M., Nowakowski, P., Turoboś, F. (2021). On functions preserving products of certain classes of semimetric spaces. Tatra Mountains Mathematical Publications, 78(1), 175-198. 1210-3195. DOI: https://doi.org/ 10.2478/tmmp-2021-0013
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 14. 10. 2021
Verejná licencia:
https://creativecommons.org/licenses/by-nc-nd/4.0/