Pre-apartness structures on spaces of functions

Authors:
D. S. Bridges;L. S. Vı^ţă
Affiliations:
Department of Mathematics & Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand;Department of Mathematics & Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
Venue:
Journal of Complexity
Year:
2006

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Abstract

Pre-apartness structures are defined on Y^X, where X is an inhabited set and Y a uniform space. These structures clarify the discussion of proximal and uniform convergence in the constructive theory of apartness spaces.