Maps that preserve left (right) $K$-Cauchy sequences

Abstract

It is well-known that on quasi-pseudometric space (X, q), every q s -Cauchy sequence is left (or right) K-Cauchy sequence but the converse does not hold in general. In this article, we study a class of maps that preserve left (right) K-Cauchy sequences that we call left (right) K-Cauchy sequentially-regular maps. Moreover, we characterize totally bounded sets on a quasi-pseudometric space in terms of maps that preserve left K-Cauchy and right K-Cauchy sequences and uniformly locally semi-Lipschitz maps.