p-topological andp-regular: dual notions in convergence theory
1999 ◽
Vol 22
(1)
◽
pp. 1-12
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Keyword(s):
The natural duality between topological and regular, both considered as convergence space properties, extends naturally top-regular convergence spaces, resulting in the new concept of ap-topological convergence space. Taking advantage of this duality, the behavior ofp-topological andp-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.
Keyword(s):
1987 ◽
Vol 94
(6)
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pp. 534-536
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2019 ◽
Vol 235
(3)
◽
pp. 1877-1887
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2020 ◽
Vol 36
(3)
◽
pp. 679-687
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Keyword(s):
1993 ◽
Vol 30
(02)
◽
pp. 330-340
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Keyword(s):