1999/02/21 by Scott A. Wilde, D. C. Kent
Mathematics · #math.GN #msc:54A20 #msc:54A10 #msc:54D10
published as Internat. J. Math. & Math. Sci. 22 (1999), 1-12 · 12 pages in Acrobat 3.0 PDF format
arxiv created 1999/02/21 · arxiv updated 2009/11/30
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.