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

• Main Authors: Scott A. Wilde, D. C. Kent
• Format: Article
• Language: English
• Published: Hindawi Limited 1999-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Subjects: Convergence space; interior map; closure map; p-topological; p-regular; initial structure; final structure; topological series; regularity series.
• Online Access: http://dx.doi.org/10.1155/S0161171299220017

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.