Articles

Lattice-Valued Cauchy Spaces and Completion

Published in: Quaestiones Mathematicae
Volume 33 , issue 1 , 2010 , pages: 53–74

DOI: 10.2989/16073601003718255

Author(s): Gunther Jäger Department of Statistics, South Africa

Keywords: L-fuzzy convergence , L-topology , L-filter , L-limit space , L-Cauchy space , L-Cauchy filter , L-uniform convergence space , probabilistic Cauchy space , completeness , completion

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Abstract

We define lattice-valued Cauchy spaces. The category of these spaces is topological over SET and cartesian closed. Special examples are lattice-valued uniform convergence spaces and probabilistic Cauchy spaces. We further define completeness and give a completion for these spaces which has the property that Cauchy continuous mappings between spaces can be extended to Cauchy-continuous mappings between their completions.

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