Abstract and concrete categories
Abstract and concrete categories
Semi-proximity continuous functions in digital images
Pattern Recognition Letters
A new definition of neighborhood of a point in multi-dimensional space
Pattern Recognition Letters
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Nearness of Objects: Extension of Approximation Space Model
Fundamenta Informaticae - Special Issue on Concurrency Specification and Programming (CS&P)
Approximation Spaces and Nearness Type Structures
Fundamenta Informaticae - Special Issue on Concurrency Specification and Programming (CS&P)
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This paper establishes an explicit embedding functor from the category of the proximity spaces into the category of nearness spaces. This is done by defining methods to constructively inducing a proximity structure with a given nearness structure and vis versa. Those induction methods provide useful tools to understand the inter-relations and to translate the result between the two types of spaces.