Two subcategories of apartness spaces

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Abstract

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.

Highlights

► 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.

MSC

03F65
54E05

Keywords

Constructive mathematics
Neighbourhood space
Uniform space
Apartness space
Adjunction

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