Apartness, Topology, and Uniformity: a Constructive View

The theory of apartness spaces, and their relation to topological spaces (in the point--set case) and uniform spaces (in the set--set case), is sketched. New notions of local decomposability and regularity are investigated, and the latter is used to produce an example of a classically metrisable apartness on R that cannot be induced constructively by even a uniform structure.

• Type: Journal
• Year: 2002
• Where: MLQ
• Authors: Douglas S. Bridges, Peter Schuster, Luminita Vîta
• Keywords: Apartness Spaces, Local Decomposability, MLQ 2002, Topological Spaces