一类半度量空间的保积函数
On functions preserving products of certain classes of semimetric spaces
摘要：
在本文中，我们继续研究Borsík和Doboeton函数，使我们能够引入一个度量的产品的度量空间。在本文中，我们扩大了他们的范围更广泛的空间类，通常不满足三角不等式，虽然他们往往满足一些较弱形式的这一公理。特别地，我们研究了保持$b$ -度量不等式的函数的行为。我们提供了Borsík和Dobobovich的结果的类似物，调整到新的，更广泛的设置。我们得到的结果说明了大量的例子。此外，新引入的家庭的功能与那些已经从文献中已知的连接进行了研究。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
