Abstract
A nearness space is Cauchy complete if every regular Cauchy filter on the space is convergent. We show that the category CCNear 2 of Cauchy complete N 2 spaces is reflective in the category Near 2 C of N 2-spaces and Cauchy maps and that the reflection of an N 2-space is given by the strict extension associated with regular Cauchy filters on the space.
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Hong, S.S., Kim, Y.K. Cauchy Complete Nearness Spaces. Applied Categorical Structures 8, 271–277 (2000). https://doi.org/10.1023/A:1008709313586
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DOI: https://doi.org/10.1023/A:1008709313586