On Functions Preserving Products of Certain Classes of Semimetric Spaces

Abstract In the paper, we continue research of Borsík and Doboš on functions which allow us to introduce a metric product spaces. We extend their scope broader class spaces usually fail satisfy triangle inequality, albeit they tend some weaker form this axiom. particular, examine behavior preserving b -metric inequality. provide analogues results adjusted new setting. The obtained are illustrated with multitude examples. Furthermore, connections newly introduced families ones already known from literature investigated.