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p-topological and p-regular: dual notions in convergence theory | | Scott A. Wilde
; D. C. Kent
; | | Date: |
21 Feb 1999 | | Journal: | Internat. J. Math. & Math. Sci. 22 (1999), 1-12 | | Subject: | General Topology MSC-class: 54A20, 54A10, 54D10 | math.GN | | Abstract: | The natural duality between "topological" and "regular," both considered as convergence space properties, extends naturally to p-regular convergence spaces, resulting in the new concept of a p-topological convergence space. Taking advantage of this duality, the behavior of p-topological and p-regular convergence spaces is explored, with particular emphasis on the former, since they have not been previously studied. Their study leads to the new notion of a neighborhood operator for filters, which in turn leads to an especially simple characterization of a topology in terms of convergence criteria. Applications include the topological and regularity series of a convergence space. | | Source: | arXiv, math.GN/9902120 | | Services: | Forum | Review | PDF | Favorites | |
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