The notions of closedness and D-connectedness in quantale-valued approach spaces

In this paper, we characterize local T_{۰} and T_{۱} quantale-valued gauge spaces, show how these concepts are related to each other and apply them to \mathcal{L}-approach distance spaces and \mathcal{L}-approach system spaces. Furthermore, we give the characterization of a closed point and D-connectedness in quantale-valued gauge spaces. Finally, we compare all these concepts to each other.

کلیدواژه ها:

mathcal{L}-approach distance space ، mathcal{L}-gauge space ، topological category ، Separation ، closedness ، D-connectedness