<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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 <italic>b</italic>-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.</p>
</abstract>

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.

On Functions Preserving Products of Certain Classes of Semimetric Spaces

Institute of Mathematics, Czech Academy of Sciences

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On Functions Preserving Products of Certain Classes of Semimetric Spaces"}

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...

On Functions Preserving Products of Certain Classes of Semimetric Spaces

Published Online: Jan 01, 2022

Page range: 175 - 198

Received: Jan 05, 2021

DOI: https://doi.org/10.2478/tmmp-2021-0013

Keywords
semimetrics, metric-preserving functions, -metrics, subadditive functions

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On Functions Preserving Products of Certain Classes of Semimetric Spaces

Published Online: Jan 01, 2022

Page range: 175 - 198

Received: Jan 05, 2021

DOI: https://doi.org/10.2478/tmmp-2021-0013

Keywordssemimetrics, metric-preserving functions, -metrics, subadditive functions

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
semimetrics, metric-preserving functions, -metrics, subadditive functions