A NOTE RELATED TO A PAPER OF NOIRI

Ilija Kovacevi\'c

Abstract: 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.

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