Completeness in Continuity Spaces
نویسنده
چکیده
1.3. De nition. ABSTRACT. We apply enriched category theory to study Cauchy completeness in continuity spaces. Our main result is the equivalence in continuity spaces of the category theoretic and the uniform notions of Cauchy completeness. This theorem, which generalizes a result of Lawvere for quasi-metric spaces, makes a natural connection between the category-theoretic and topological aspects of continuity spaces, and provides a simple construction of the Cauchy completion of a continuity space.
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