Results 11 to 20 of about 82 (79)

Fuzzy properties in fuzzy convergence spaces

International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 12, Page 737-748, 2002., 2002
Based on the concept of limit of prefilters and residual implication, several notions in fuzzy topology are fuzzyfied in the sense that, for each notion, the degree to which it is fulfilled is considered. We establish therefore theories of degrees of compactness and relative compactness, of closedness, and of continuity.
Gunther Jäger
wiley   +1 more source

γ‐sets and γ‐continuous functions

International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 3, Page 177-181, 2002., 2002
We introduce a new class of sets, called γ‐sets, and the notion of γ‐continuity and investigate some properties and characterizations. In particular, γ‐sets and γ‐continuity are used to extend known results for semi‐open sets and semi‐continuity.
Won Keun Min
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

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
doaj   +1 more source