Results 11 to 20 of about 364 (52)
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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On the different kinds of separability of the space of Borel functions
Open Mathematics, 2018 In paper we prove that:
Osipov Alexander V.
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On selective sequential separability of function spaces with the compact-open topology [PDF]
, 2018 For a Tychonoff space $X$, we denote by $C_k(X)$ the space of all real-valued continuous functions on X with the compact-open topology. In this paper, we have gave characterization for $C_k(X)$ to satisfy $S_{fin}(S, S)$.Comment: 9 pages.
Osipov, Alexander V.
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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 space of upper semicontinuous functions [PDF]
, 2018 For a Tychonoff space $X$, we will denote by $USC_{p}(X)$ ($B_1(X)$) a set of all real-valued upper semicontinuous functions (a set of all Baire functions of class 1) defined on $X$ endowed with the pointwise convergence topology.
Osipov, Alexander V. +1 more
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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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