论文标题
关于保留某些类别半学空间的产品的功能
On functions preserving products of certain classes of semimetric spaces
论文作者
论文摘要
在论文中，我们继续研究Borsík和Doboš对功能的研究，这些功能使我们能够向度量空间的产物引入度量标准。在本文中，我们将它们的范围扩展到通常无法满足三角形不平等的更广泛的空间范围，尽管它们倾向于满足这种公理的某种弱形式。特别是，我们研究了保留$ b $ metric不平等的功能的行为。我们提供了Borsík和Doboš结果的类似物，并调整为新的，更广泛的环境。我们获得的结果用众多示例说明了。此外，研究了新引入的功能系列与从文献中已经知道的功能的联系。
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. In this paper we extend their scope on 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.
