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On decomposition of continuity in topological spaces. (English) Zbl 0724.54012
In this paper t-sets are introduced and used to define \({\mathcal B}\)-sets, which are used to define \({\mathcal B}\)-continuity. Let (X,T) be a topological space and let \(S\subset X\). Then S is a t-set iff \(Int(C1(S))=Int(S)\) and S is a \({\mathcal B}\)-set iff there exists a \(U\in T\) and a t-set A in X such that \(S=U\cap A\). A mapping f:(X,T)\(\to (Y,S)\) is \({\mathcal B}\)-continuous iff for each \(V\in S\), \(f^{-1}(V)\) is a \({\mathcal B}\)-set in X. Results in the paper include (1) f:(X,T)\(\to (Y,S)\) is continuous iff it is both pre-continuous and \({\mathcal B}\)-continuous, and (2) f:(X,T)\(\to (Y,S)\) is open iff it is both pre-open and \({\mathcal B}\)- open.

MSC:
54C08 Weak and generalized continuity
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