Abstract
A nearness frame is Cauchy complete if every regular Cauchy filter on the nearness frame is convergent and we show that the categoryCCNFrm of Cauchy complete nearness frames is coreflective in the categoryNFrmC of nearness frames and Cauchy homomorphisms and that the coreflection of a nearness frame is given by the strict extension associated with regular Cauchy filters on the nearness frame. Using the same completion, we show that the categoryCCSNFrm of Cauchy complete strong nearness frames is coreflective in the categorySNFrm of strong nearness frames and uniform homomorphisms.
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References
Adámek, J., Herrlich, H., and Strecker, G. E.:Abstract and Concrete Categories, Wiley Interscience, New York, 1990.
Banaschewski, B.:Completion in Point-Free Topology, Math. Monographs of the University of Cape Town, to appear.
Banaschewski, B. and Hong, S. S.: Filters and strict extensions of frames, Preprint, 1995.
Banaschewski, B. and Pultr, A.: Cauchy points of uniform and nearness frames, Preprint, 1994.
Hong, S. S.: Simple extensions of frames,Proc. Recent Devel. of Gen. Top. and its Appl., Math. Res. 67 (1992), 156–159.
Hong, S. S.: Convergence in frames,Kyungpook Math. J. 35 (1995), 85–91.
Johnstone, P. T.:Stone Spaces, Cambridge Stud. Adv. Math.3, 1982.
Paseka, J. and Šmarda, B.:T 2-frames and almost compact frames,Czech. Math. J. 42 (1992), 385–402.
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Hong, S.S., Kim, Y.K. Cauchy completions of nearness frames. Appl Categor Struct 3, 371–377 (1995). https://doi.org/10.1007/BF00872906
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DOI: https://doi.org/10.1007/BF00872906