Results 21 to 30 of about 79 (77)
Regular‐uniform convergence and the open‐open topology
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 5, Page 357-360, 2001., 2001 In 1994, Bânzaru introduced the concept of regular‐uniform, or r‐uniform, convergence on a family of functions. We discuss the relationship between this topology and the open‐open topology, which was described in 1993 by Porter, on various collections of functions.
Kathryn F. Porter
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Convergence structures in M-fuzzifying convex spaces [PDF]
, 2021 By means of M-fuzzifying convex lters, fuzzy convergence structures in the framework of M-fuzzifying convex spaces are proposed, which are called M- fuzzifying convergence structures. It is shown that there is a Galois correspondence between the category
Pang, Bin
core
An Ascoli theorem for sequential spaces
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 5, Page 303-315, 2001., 2001 Ascoli theorems characterize “precompact” subsets of the set of morphisms between two objects of a category in terms of “equicontinuity” and “pointwise precompactness,” with appropriate definitions of precompactness and equicontinuity in the studied category.
Gert Sonck
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Compacity in narrow limit tower spaces
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 6, Page 359-369, 2001., 2001 We introduce a limit tower structure on the space of all bounded Radon measures on a completely regular space and we extend the Prohorov′s theorem of narrow compactness. In the particular case of Polish spaces, we give a sequential version of this extension.
Liviu C. Florescu
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On 3‐topological version of θ‐regularity
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 6, Page 393-398, 2000., 2000 We modify the concept of θ‐regularity for spaces with 2 and 3 topologies. The new, more general property is fully preserved by sums and products. Using some bitopological reductions of this property, Michael′s theorem for several variants of bitopological paracompactness is proved.
Martin M. Kovár
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A note on Raghavan‐Reilly′s pairwise paracompactness
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 2, Page 139-143, 2000., 2000 The bitopological unstability of RR‐pairwise paracompactness in presence of pairwise Hausdorff separation axiom is caused by a bitopological property which is much weaker and more local than RR‐pairwise paracompactness. We slightly generalize some Michael′s constructions and characterize RR‐pairwise paracompactness in terms of bitopological θ ...
Martin M. Kovár
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Completion of a Cauchy space without the T2‐restriction on the space
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 3, Page 163-172, 2000., 2000 A completion of a Cauchy space is obtained without the T2 restriction on the space. This completion enjoys the universal property as well. The class of all Cauchy spaces with a special class of morphisms called s‐maps form a subcategory CHY′ of CHY. A completion functor is defined for this subcategory. The completion subcategory of CHY′ turns out to be
Nandita Rath
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p‐topological and p‐regular: dual notions in convergence theory
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 1-12, 1999., 1999 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 ...
Scott A. Wilde, D. C. Kent
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A result for O2-convergence to be topological in posets
Open Mathematics, 2016 In this paper, the α waybelow relation, which is determined by O2-convergence, is characterized by the order on a poset, and a sufficient and necessary condition for O2-convergence to be topological is obtained.
Li Qingguo, Zou Zhiwei
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International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 3, Page 659-665, 1999., 1999 First, we introduce sequential convergence structures and characterize Fréchet spaces and continuous functions in Fréchet spaces using these structures. Second, we give sufficient conditions for the expansion of a topological space by the sequential closure operator to be a Fréchet space and also a sufficient condition for a simple expansion of a ...
Woo Chorl Hong
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