Lattice-Valued Cauchy Spaces and Completion
Gunther Jäger · Quaestiones Mathematicae · 2010
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.