Geodesic
A Note Related to a Paper of Noiri
Publications de l'Institut Mathématique, _N_S_36 (1984) no. 50, p. 103

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. 
@article{PIM_1984_N_S_36_50_a14,
     author = {Ilija Kova\v{c}evi\'c},
     title = {A {Note} {Related} to a {Paper} of {Noiri}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {103 },
     publisher = {mathdoc},
     volume = {_N_S_36},
     number = {50},
     year = {1984},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1984_N_S_36_50_a14/}
}
TY  - JOUR
AU  - Ilija Kovačević
TI  - A Note Related to a Paper of Noiri
JO  - Publications de l'Institut Mathématique
PY  - 1984
SP  - 103 
VL  - _N_S_36
IS  - 50
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PIM_1984_N_S_36_50_a14/
LA  - en
ID  - PIM_1984_N_S_36_50_a14
ER  - 
%0 Journal Article
%A Ilija Kovačević
%T A Note Related to a Paper of Noiri
%J Publications de l'Institut Mathématique
%D 1984
%P 103 
%V _N_S_36
%N 50
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PIM_1984_N_S_36_50_a14/
%G en
%F PIM_1984_N_S_36_50_a14
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/