Approach Merotopological Spaces and their Completion

Abstract EN

This paper introduces the concept of an approach merotopological space and studies its category-theoretic properties.

Various topological categories are shown to be embedded into the category whose objects are approach merotopological spaces.

The order structure of the family of all approach merotopologies on a nonempty set is discussed.

Employing the theory of bunches, bunch completion of an approach merotopological space is constructed.

The present study is a unified look at the completion of metric spaces, approach spaces, nearness spaces, merotopological spaces, and approach merotopological spaces.