Cauchy Complete Nearness Spaces

Sung Sa Hong () and Young Kyoung Kim
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Sung Sa Hong: Sogang University, Department of Mathematics
Young Kyoung Kim: Sogang University, Department of Mathematics

A chapter in Papers in Honour of Bernhard Banaschewski, 2000, pp 271-277 from Springer

Abstract: 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.

Keywords: nearness spaces; regular Cauchy filters; Cauchy complete nearness spaces; Cauchy completions of nearness spaces; Cauchy maps.; nearness spaces; 18A40; 54D35; 54E17 (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-2529-3_15

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DOI: 10.1007/978-94-017-2529-3_15

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