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A note on weakly quasi continuous functions. (English) Zbl 0671.54024

Summary: V. Popa and C. Stan [Stud. Cercet Mat. 25, 41-43 (1973; Zbl 0255.54008)] have shown that a function f: \(X\to Y\) is weakly quasi continuous if and only if \(f^{-1}(Cl(V))\subset Cl(Int(f^{- 1}(Cl(V))))\) for every open set V of Y. By utilizing this result, the present author [Int. J. Math. Math. Sci. 10, 483-490 (1987; Zbl 0638.54012)] showed that a function f: \(X\to Y\) is weakly quasi continuous if and only if for every regular closed set F of Y, \(f^{-1}(F)\) is semi-open in X. In this note, the author shows that these results are false and corrects the proofs of Theorem 6.1.7 and Lemma 6.4.4 of the second cited paper.

MSC:

54C08 Weak and generalized continuity
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