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The natural duality between topological and regular, both considered as convergence space properties, extendsnaturally 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

international journal of mathematics and mathematical sciences

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$p$"><mml:mi>p</mml:mi></mml:math>-topological and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$p$"><mml:mi>p</mml:mi></mml:math>-regular: dual notions in convergence theory

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