On functions preserving products of certain classes of semimetric spaces

0553968 - MÚ 2022 RIV SK eng J - Journal Article
Nowakowski, Piotr
On functions preserving products of certain classes of semimetric spaces.
Tatra Mountains Mathematical Publications. Roč. 78, č. 1 (2021), s. 175-198. ISSN 1210-3195
Institutional support: RVO:67985840
Keywords : semimetrics * metric-preserving functions * b-metrics * subadditive functions
OECD category: Pure mathematics
Method of publishing: Open access
https://doi.org/10.2478/tmmp-2021-0013

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. W 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.
Permanent Link: http://hdl.handle.net/11104/0328630