On the quasi-uniform convergence

• Autorzy: Drozdowski R. , Jędrzejewski J. , Sochaczewska A.
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

convergence; sequence of functions; topological space; uniform convergence

PL

konwergencja; sekwencje funkcyjne; przestrzeń topologiczna; jednolita konwergencja

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2011
• Tom: Vol. 16
• Strony: 19--22
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Drozdowski R.

• Institute of Mathematics, Academia Pomeraniensis ul. Arciszewskiego 22b, 76-200 Słupsk, Poland

autor

Jędrzejewski J.

• Institute of Mathematics and Computer Science Jan Długosz University in Częstochowa al.Armii Krajowej 13/15, 42-200 Częstochowa, Poland

autor

Sochaczewska A.

• 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.