Approach Merotopological Spaces and their Completion

This paper introduces the concept of an approach merotopological space and studies its categorytheoretic 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 approachmerotopologies 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.