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On quasi-oscillation for symmetrical quasi-continuity

In: Tatra Mountains Mathematical Publications, vol. 34, no. 2
Irena Domnik
Detaily:
Rok, strany: 2006, 61 - 69
O článku:
A classical oscillation (quasi-oscillation) characterizes the set of all points at which a function with values in a metric space is continuous (quasi-continuous). These conditions were introduced in [J. Borsík: Oscillation for quasicontinuity, Tatra Mt. Math. Publ. 14, (1998), 117–125], [J. Borsík: On quasioscillation, Tatra Mt. Math. Publ. 2, (1993), 25–36], [J. Ewert: Superpositions of oscillations and quasi-oscillations, Acta Math. Hungar. {bf 101}, (2003), 13–19], [P. Kostyrko: Some properties of oscillation, Math. Slovaca, 30, (1980), 157–162]. For the functions of two variables the symmetrical quasi-continuity (with respect to $x$ and $y$) can be considered. In this paper we define a quasi-oscillation for symmetrically quasi-continuous functions. We will give properties of this oscillation and a characterization of the symmetrical quasi-continuity with respect to $x$ (to $y$). Furthermore, we will study the convergence of a net of quasi-oscillations. Moreover, relationships between sets of points of continuity, symmetrical quasi-continuity, and quasi-continuity of the function are considered. For real function of two variables the Baire type (with respect to $x$ and $y$) functions are introduced.
Ako citovať:
ISO 690:
Domnik, I. 2006. On quasi-oscillation for symmetrical quasi-continuity. In Tatra Mountains Mathematical Publications, vol. 34, no.2, pp. 61-69. 1210-3195.

APA:
Domnik, I. (2006). On quasi-oscillation for symmetrical quasi-continuity. Tatra Mountains Mathematical Publications, 34(2), 61-69. 1210-3195.