Results 11 to 20 of about 61 (61)
Aspects of complete uniform spreads in frames
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 4, Page 193-199, 2002., 2002 We give a new notion of a complete uniform spread in terms of a relative kind of uniform local connectedness. Properties of this type of (uniform) connectedness are discussed. It is also shown that our concept of complete spread is equivalent to that of Hunt (1982).
Hlengani James Siweya
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Transitivity in uniform approach theory
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 12, Page 707-720, 2002., 2002 We introduce a notion of transitivity for approach uniformities and approach uniform convergence spaces, yielding reflective subconstructs of AUnif and AUCS. Further, we investigate how these new categories are related to uACHY, uACHY U , and uMET, and we show that these relationships are similar to those in the classical case.
Y. J. Lee, B. Windels
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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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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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The prime filter theorem of lattice implication algebras
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 2, Page 115-118, 2001., 2001 Using a special set x−1F, we give an equivalent condition for a filter to be prime, and applying this result, we provide the prime filter theorem in lattice implication ...
Young Bae Jun
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Covering properties for LQ𝒰 s with nested bases
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 8, Page 549-558, 2001., 2001 This paper deals with problems on LQ𝒰 spaces which have a nested base; among others we give conditions so that a space (X, τ1, τ2) admits an LQ𝒰𝒰 which generates τ1 and 𝒰−1τ2, and give necessary and sufficient conditions for a space to be quasi‐metrizable, related to concrete covering properties. We also give a Stone′s type characterization of pairwise
A. Andrikopoulos, J. N. Stabakis
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Precompactness and total boundedness in products of metric spaces
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 11, Page 663-672, 2001., 2001 We show that the canonical quantifications of uniform properties such as precompactness and total boundedness, which were already studied by Kuratowski and Hausdorff in the setting of complete metric spaces, can be generalized in the setting of products of metric spaces in an intuitively appealing way.
Bart Windels
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International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 11, Page 729-739, 2000., 2000 Approach uniformities were introduced in Lowen and Windels (1998) as the canonical generalization of both metric spaces and uniform spaces. This text presents in this new context of “quantitative” uniform spaces, a reflective completion theory which generalizes the well‐known completions of metric and uniform spaces. This completion behaves nicely with
Robert Lowen, Bart Windels
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International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 5, Page 295-304, 2000., 2000 This paper gives a further development of p‐regular completion theory, including a study of p‐regular Reed completions, the role of diagonal axioms, and the relationship between p‐regular and p‐topological completions.
Darrell C. Kent, Jennifer Wig
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Fantastic filters of lattice implication algebras
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 4, Page 277-281, 2000., 2000 The notion of a fantastic filter in a lattice implication algebra is introduced, and the relations among filter, positive implicative filter, and fantastic filter are given. We investigate an equivalent condition for a filter to be fantastic, and state an extension property for fantastic filter.
Young Bae Jun
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