Apartness, compactness and nearness
We investigate constructively a pre-apartness structure that is classically important in the characterisation of compact proximity spaces, and that may help identify a good constructive notion of compactness for not-necessarily-uniform apartness spaces. In addition, we produce what may be the right notion of "nearness" in the theory of apartness Spaces. (c) 2008 Elsevier B.V. All rights reserved.
apartness compact near constructive totally bounded