Results 21 to 30 of about 61 (61)
p‐topological Cauchy completions
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 3, Page 497-509, 1999., 1999 The duality between “regular” and “topological” as convergence space properties extends in a natural way to the more general properties “p‐regular” and “p‐topological.” Since earlier papers have investigated regular, p‐regular, and topological Cauchy completions, we hereby initiate a study of p‐topological Cauchy completions.
J. Wig, D. C. Kent
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A Unif: A common supercategory of pMET and Unif
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 1, Page 1-18, 1998., 1997 In order to have a topological category that contains both pMET and Unif in a nice way (and therefore combines quantitative and uniform concepts), approach uniformities are introduced. Approach uniformities uniformize the so‐called approach spaces, introduced in Lowen [8]. Different characterizations of approach uniformities are formulated.
R. Lowen, B. Windels
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(Quasi)‐uniformities on the set of bounded maps
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 693-696, 1994., 1993 From real analysis it is known that if a sequence {fn, n ∈ ℕ} of real‐valued functions defined and bounded on X ⊂ ℝ converges uniformly to f, then f is also bounded and the sequence {fn, n ∈ ℕ}. In the present paper we generalize results as the above using (quasi)‐uniform structures.
Basil K. Papadopoulos
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Non archimedean metric induced fuzzy uniform spaces
International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 1, Page 47-59, 1989., 1989 It is shown that the category of non‐Archimedean metric spaces with 1‐Lipschitz maps can be embedded as a coreflective non‐bireflective subcategory in the category of fuzzy uniform spaces. Consequential characterizations of topological and uniform properties are derived.
R. Lowen, A. K. Srivastava, p. Wuyts
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Order compatibility for Cauchy spaces and convergence spaces
International Journal of Mathematics and Mathematical Sciences, Volume 10, Issue 2, Page 209-216, 1987., 1987 A Cauchy structure and a preorder on the same set are said to be compatible if both arise from the same quasi‐uniform convergence structure on X. Howover, there are two natural ways to derive the former structures from the latter, leading to strong and weak notions of order compatibility for Cauchy spaces.
D. C. Kent, Reino Vainio
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On some fixed point theorems in Banach spaces
International Journal of Mathematics and Mathematical Sciences, Volume 5, Issue 1, Page 113-122, 1982., 1980 In this paper, some fixed point theorems are proved for multi‐mappings as well as a pair of mappings. These extend certain known results due to Kirk, Browder, Kanna, Ćirić and Rhoades.
D. V. Pai, P. Veeramani
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International Journal of Mathematics and Mathematical Sciences, Volume 5, Issue 3, Page 513-527, 1982., 1982 A family C of filters on a set X is uniformizable if there is a uniformity on X such that C is its collection of Cauchy filters. Using the theory of completions and Cauchy continuous maps for Cauchy spaces, we obtain characterizations of uniformizable Cauchy spaces. In particular, given a Cauchy structure C on X we investigate under what conditions the
Eva Lowen-Colebunders
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A completion functor for Cauchy groups
International Journal of Mathematics and Mathematical Sciences, Volume 4, Issue 1, Page 55-65, 1981., 1981 A completion functor is constructed on the category of completely normal Cauchy groups and Cauchy‐continuous homomorphisms. A competion functor is also obtained for a corresponding category of convergence groups.
R. Fric, D. C. Kent
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, 1988 International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 3, Page 435-440, 1989.
D. Baboolal
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On the Strict Completion of a Nearness Space
, 2004 The strict completion of a nearness space was constructed in 1974 in Herrlich's original paper on nearness. we present an external characterization of this completion. Among the consequences of this result is the fact that for nearness spaces X and
Bentley, HL, Herrlich, H
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