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Universally polygonally approximable functions

100%

Evans. M. J. , Humke P. D. , O`Malley R. J.

Journal of Applied Analysis

2000

tom Vol. 6, nr 1

25-45

It has recently been established that any Baire class one function f : [0,1] -> R can be represented as the pointwise limit of a sequence of polygonal functions whose vertices lie on the graph of f. Here we investigate the subclass of Baire class one functions having the additional property that for every dense subset D of [0,1], the first coordinates of the vertices of the polygonal functions can be chosen from D.

On sets determined by sequences of quasi-continuous functions

84%

Wesołowska J.

Journal of Applied Analysis

2001

tom 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

84%

Grande Z.

Journal of Applied Analysis

2001

tom 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.