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

Scott A. Wilde and D. C. Kent

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-12

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.

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:826210

DOI: 10.1155/S0161171299220017

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