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On the quasi-uniform convergence

Drozdowski R., Jędrzejewski J., Sochaczewska A.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2011

Vol. 16

19--22

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].

On sets determined by sequences of quasi-continuous functions

Wesołowska J.

Journal of Applied Analysis

2001

Vol. 7, nr 2

271-283

The aim of the paper is to characterize those sets of points at which sequence of real functions from a given class F converges as well as sets of points of convergence to infinity of such sequences. As F we consider quasi-continuous functions and some other subclasses of Baire measurable functions.

On sequences of upper and lower semi-quasicontinuous functions

Grande Z.

Journal of Applied Analysis

2001

Vol. 7, nr 2

235-242

In this article we investigate the pointwise, discrete and transfinite convergences in the classes of real functions defined on topological spaces which are upper and lower quasicontinuous at each point.