标题：<mml:math alttext="$p$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-topological and <mml:math alttext="$p$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-regular: dual notions in convergence theory
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1999
卷号：22
DOI：10.1155/S0161171299220017
出版社：Hindawi Publishing Corporation
摘要：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.
