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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
Full Text:
##### References:
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