Two subcategories of apartness spaces

Compactness in apartness spaces?

In this note, we establish some results which suggest a possible solution to the problem of finding the right constructive notion of compactness in the context of a not–necessarily–uniform apartness space.

Precompact Apartness Spaces

We present a notion of precompactness, and study some of its properties, in the context of apartness spaces whose apartness structure is not necessarily induced by any uniform one. The presentation lies entirely with a Bishop-style constructive framework, and is a contribution to the ongoing development of the constructive theories of apartness and uniformity.

Quasi-apartness and neighbourhood spaces

Contributions to Pointfree Topology and Apartness Spaces

Hedin, A. 2011. Contributions to Pointfree Topology and Apartness Spaces. Department of Mathematics. Uppsala Dissertations in Mathematics 71. 40 pp. Uppsala. The work in this thesis contains some contributions to constructive point-free topology and the theory of apartness spaces. The first two papers deal with constructive domain theory using formal topology. In Paper I we focus on the notion ...

Proximal and uniform convergence on apartness spaces

The main purpose of this paper is to investigate constructively the relationship between proximal convergence, uniform sequential convergence and uniform convergence for sequences of mappings between apartness spaces. It is also shown that if the second space satisfies the Efremovic axiom, then proximal convergence preserves strong continuity. Mathematics Subject Classification: 54E05, 03F60