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On ∞-entropy points in real analysis

Korczak-Kubiak E., Loranty A., Pawlak R. J.

Opuscula Mathematica

2014

Vol. 34, no. 4

799--812

We will consider ∞-entropy points in the context of the possibilities of approximation mappings by the functions having ∞-entropy points and belonging to essential (from the point of view of real analysis theory) classes of functions: almost continuous, Darboux Baire one and approximately continuous functions.

Almost continuity, regular set-connected mappings and some separation axioms

Duszyński Z.

Demonstratio Mathematica

2006

Vol. 39, nr 4

939-948

Let f : (X, r ) approaches (Y,sigma) be a mapping, let (X, rs) denote the topological space generated by the family of all regular open subsets of (X, r ) and let fxs : (X, rs) !approaches (Y, sigma) be defined by fxs (x) = f(x) for each x is an element of X. In the paper relationships between almost continuity of f, almost continuity of fxs and some other types of mappings (r.s.c. mappings in particular) are studied.