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

Authors : Olivier OLELA OTAFUDU

Pages : 1466-1476

Doi:10.15672/hujms.815689

View : 12 | Download : 5

Publication Date : 2021-10-15

Article Type : Research Paper

Abstract : It is well-known that on quasi-pseudometric space $insert ignore into journalissuearticles values(X,q);$, every $q^s$-Cauchy sequence is left insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(right); $K$-Cauchy sequences that we call left insert ignore into journalissuearticles values(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.
Keywords : Cauchy sequential regularity, left K Cauchy, bornology, uniform continuity, total boundedness