Abstract:It is a meaningful issue that under what condition neighborhoods induced by a covering are equal to the covering itself. A necessary and sufficient condition for this issue has been provided by some scholars. In this paper, through a counter-example, we firstly point out the necessary and sufficient condition is false. Second, we present a necessary and sufficient condition for this issue. Third, we concentrate on the inverse issue of computing neighborhoods by a covering, namely giving an arbitrary covering, … Show more
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