Bounded proximities and related nearness

Abstract

The new created concept Bounded Topology, a convenient foundation for topology, (see [9]) deals with a lot kind of structures examined by topologists in the past: Especially, generalized convergence spaces, now de ned as b-convergences in [8], appear in a new context with the same of its convenient properties like being a strong topological universe. In this realm we now consider bounded proximities and related nearness by generalizing LODATO spaces and nearness spaces to so called paranear spaces. Its subclass of paraclan spaces is in one-to-one correspondence to a certain kind of symmetric, strict topological extension. Hence, Lodato's famous theorem [10] and Bently's framework [2] about bunch determined nearness spaces can be also dealt with.

Keywords: LODATO space, nearness, paranearness, paraclan spaces

Quaestiones Mathematicae 36(2013), 381-387