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On some classes of sets in extremally disconnected spaces

Duszyński Z.

Demonstratio Mathematica

2011

Vol. 44, nr 1

169--180

In the present paper several characterizations of the classical notion of extremally disconnected spaces are obtained. A few relationships for finite products of extremally disconnected spaces are also studied.

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.