Results 11 to 20 of about 66 (65)
Journal of Function Spaces, Volume 7, Issue 1, Page 61-89, 2009., 2009 In connection with application to various problems of operator theory, we study almost monotonic functions w(x, r) depending on a parameter x which runs a metric measure space X, and the so called index numbers m(w, x), M(w, x) of such functions, and consider some generalized Zygmund, Bary, Lozinskii and Stechkin conditions.
Natasha Samko, Vladimir D. Stepanov
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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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Quasi‐pseudometrizability of the point open ordered spaces and the compact open ordered spaces
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 7, Page 385-392, 2001., 2001 We determine conditions for quasi‐pseudometrizability of the point open ordered spaces and the compact open ordered spaces. This generalizes the results on metrizability of the point open topology and the compact open topology for function spaces. We also study conditions for complete quasi‐pseudometrizability.
Koena Rufus Nailana
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A note on connectedness in cartesian closed categories
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 1, Page 101-104, 1997., 1997 Primaxily working in the category of limit spaces and continuous maps we suggest a new concept of connectivity with application in all categories where function space objects satisfy natural exponential laws. In a separate Appendix we motivate the development of a homotopy theory for spaces of real‐valued continuous maps endowed with the structure of ...
Reino Vainio
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Covariant and contravariant approaches to topology
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 621-626, 1997., 1997 This paper is an exposition of results contained in [2]. The purpose of [2] is to present a way of viewing of basic topology which unifies quite a few results and concepts previously seemed not related (quotient maps, product topology, subspace topology, separation axioms, topologies on function spaces, dimension, metrizability). The basic idea is that
Jerzy Dydak
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On some properties of the spaces of almost continuous functions
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 1, Page 19-23, 1996., 1994 In this paper we prove that, in the space 𝒜 of almost continuous functions (with the metric of uniform convergence), the set of functions of the first class of Baire is superporous at each point of this ...
Ryszard Jerzy Pawlak
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The regular open‐open topology for function spaces
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 2, Page 299-302, 1996., 1995 The regular open‐open topology, Troo, is introduced, its properties for spaces of continuous functions are discussed, and Troo is compared to Too, the open‐open topology. It is then shown that Troo on H(X), the collection of all self‐homeomorphisms on a topological space, (X, T), is equivalent to the topology induced on H(X) by a specific quasi ...
Kathryn F. Porter
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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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On Pervin′s example concerning the connected‐open topology
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 2, Page 223-226, 1990., 1990 Irudayanathan and Naimpally [1] introduced a topology for function spaces (called the connected‐open topology) which has the property that the connected functions form a closed set provided that the codomain is completely normal. Pervin [2] gave an example showing that the proviso cannot be weakened to normality.
T. B. M. McMaster
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