Lattice-Valued Cauchy Spaces and Completion

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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