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In a recent paper Abd El-Monsef et al. consider a certain topology on $2^X$ where $2^X$ is the family of all nonempty closed subsets of a given topological space $X$. Vnfortunately, several results in their paper are incorrect and so the purpose of this note is to correct, improve and expand these results. In addition, the main quesion in their paper turns out to have a quite simple answer.
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