Mathematica Eterna
Open Access

Abstract

A New Approach to the Study of Extended Metric Spaces

Surabhi Tiwari and James F. Peters

This paper studies the category theoretic aspects of ε-approach nearness spaces and ε-approach merotopic spaces, respectively, ε ∈ (0, ∞], which are useful in measuring the degree of nearness (resemblance) of objects. Such structures measure the almost nearness of two collections of subsets of a nonempty set. The categories εANear and εAMer are shown to be full supercategories of various well-known categories, including the category sT op of symmetric topological spaces and continuous maps, and the category Met∞ of extended metric spaces and nonexpansive maps. The results in this paper have important practical implications in the study of patterns in similar pictures.