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Arzelá [1] considered the weaker form of uniform convergence which is as good as uniform convergence of sequences of functions in respect to continuity of the limit of a sequence of continuous functions. Some generalization of such convergence can be found in [5]. Similar kinds of convergence of function sequences were considered in [3] and [4]. In our article we generalize those kinds of convergence for functions defined in a topological space with values in a topological space. In the article we use terminology which is explained in Engelking's monograph “General Topology” [2]. Among others, we use the notion of a star with respect to an open over. If X is a topological space and α is a cover of this space, then the star St(x, α) of a point x ϵ X with respect to the cover α is defined as the union of all the sets from α which contain the point x, i.e. [wzór].
Rocznik
Tom
Strony
19--22
Opis fizyczny
Bibliogr. 5 poz.
Twórcy
autor
- Institute of Mathematics, Academia Pomeraniensis ul. Arciszewskiego 22b, 76-200 Słupsk, Poland
autor
- Institute of Mathematics and Computer Science Jan Długosz University in Częstochowa al.Armii Krajowej 13/15, 42-200 Częstochowa, Poland
autor
- Institute of Mathematics, Academia Pomeraniensis ul. Arciszewskiego 22b, 76-200 Słupsk, Poland
Bibliografia
- [1] C. Arzelá. Sulle serie di funzioni. Mem. R. Acad. Sci. Ist. Bologna, serie 5 (8), 131-186, 701-744, 1899-1900.
- [2] R. Engelking. General Topology, PWN Warszawa 1977.
- [3] I. Kupka, V. Toma. A uniform convergence for non-uniform spaces. Publ. Math. Debrecen, 47, 299-309, 1995.
- [4] A. Sochaczewska. The strong quasi-uniform convergence. Math. Montisnigri, XV, 45-55, 2002.
- [5] B. Szökefalvi-Nagy. Introduction to Real Functions and Orthogonal Expansions. Akadémiai Kiadó, Budapest 1964.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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