International Journal of Mathematics and Mathematical Sciences (Jan 1999)

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

  • Scott A. Wilde,
  • D. C. Kent

DOI
https://doi.org/10.1155/S0161171299220017
Journal volume & issue
Vol. 22, no. 1
pp. 1 – 12

Abstract

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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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