Luminita Vîta

A constructive theory of point-set nearness

An axiomatic constructive development of the theory of nearness and apartness of a point and a set is introduced as a setting for topology.

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.

Locating subsets of a normed space

Within the framework of Bishops constructive mathematics, we give conditions under which a bounded convex subset of a uniformly smooth normed space over R is located, extending results presented recently by F. Richman and H. Ishihara for subsets of a Hilbert space.

Separation properties in neighbourhood and quasi-apartness spaces

We investigate separation properties for neighbourhood spaces in some details within a framework of constructive mathematics, and define corresponding separation properties for quasi-apartness spaces. We also deal with separation properties for spaces with inequality. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)