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On proximal convergence in uniform spaces

Luminiţa Simona Vîţă

Mathematical Logic Quarterly 49 (6):550 (2003)

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Proximal and uniform convergence on apartness spaces.Luminiţa Simona Vîţă - 2003 - Mathematical Logic Quarterly 49 (3):255.details 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. Download Export citation Bookmark 5 citations
Apartness spaces as a framework for constructive topology.Douglas Bridges & Luminia Vî - 2003 - Annals of Pure and Applied Logic 119 (1-3):61-83.details An axiomatic development of the theory of apartness and nearness of a point and a set is introduced as a framework for constructive topology. Various notions of continuity of mappings between apartness spaces are compared; the constructive independence of one of the axioms from the others is demonstrated; and the product apartness structure is defined and analysed. Download Export citation Bookmark 13 citations
Apartness spaces as a framework for constructive topology.Douglas Bridges & Luminiţa Vîţă - 2003 - Annals of Pure and Applied Logic 119 (1-3):61-83.details An axiomatic development of the theory of apartness and nearness of a point and a set is introduced as a framework for constructive topology. Various notions of continuity of mappings between apartness spaces are compared; the constructive independence of one of the axioms from the others is demonstrated; and the product apartness structure is defined and analysed. Download Export citation Bookmark 15 citations

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