In S.G. Matthews [Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197], the author introduced and studied the concept of partial metric space, and obtained a Banach type fixed point theorem on complete partial metric spaces. The present paper forms part of the study of possible extensions of met...

An axiom system for machine spaces is introduced. Time is modeled as a totally ordered monoid, thus allowing discrete, continuous, and transfinite time structures. A generalized metric on these machine spaces is defined, having values in a directedly ordered monoid. This enables the notion of ε-balls in machine space, which, for example, can be used to explore model risk and robustness in stati...

In this paper,  it is shown that the category of $L$-ordered fuzzifying convergence spaces contains the category of pretopological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory and the latter contains the category of topological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory. Also, it is proved that the category of $L$-ordered fuzzifying conver...