Geodesic
A Note Related to a Paper of Noiri
Publications de l'Institut Mathématique, _N_S_36 (1984) no. 50, p. 103 
Ilija Kovačević. A Note Related to a Paper of Noiri. Publications de l'Institut Mathématique, _N_S_36 (1984) no. 50, p. 103 . http://geodesic.mathdoc.fr/item/PIM_1984_N_S_36_50_a14/
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     title = {A {Note} {Related} to a {Paper} of {Noiri}},
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Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In [4] Noiri gave a counterexample to Lemma 1.1 in [1] which reads: If $f:X\to Y$ is an almost closed and almost continuous mapping, then $f^{-1}(V)$ is regularly open (regularly closed) in $X$ for each regularly open (regularly closed) set $V$ in $Y$. In this counterexample $f$ is not a surjection. There exists also another counterexample, where $f$ is a surjection. There exists also another counterexample, where $f$ is a surjection (Example 1 in [2]). But, Lemma A is necessarily true if a new condition is added.