p-topological and p-regular: dual notions in convergence theory

Details p-topological and p-regular: dual notions in convergence theory p-topological and p-regular: dual notions in convergence theory

1999-02-21

arxiv.org/abs/math/9902120v1

Internat. J. Math. & Math. Sci. 22 (1999), 1-12

Mathematics

General Topology

12 pages in Acrobat 3.0 PDF format

Scientific paper

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.

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