Two subcategories of apartness spaces

We introduce the notion of a topological quasi-apartness space and the notion of a uniform quasi-apartness space, and construct an adjunction between the category of topological quasi-apartness spaces and the category of neighbourhood spaces, and an adjunction between the category of uniform spaces and the category of uniform quasi-apartness spaces.

► We introduce topological apartness spaces and uniform apartness spaces. ► An adjunction between topological apartness spaces and neighbourhood spaces is found. ► We also construct an adjunction between uniform apartness spaces and uniform spaces.