Abstract:
By considering the interval (0,1) on the real line it is easy to show that it is not possible, in general, to obtain boundary of a given set by using the complementation, he closure and the interior operations on that set. Therefore one can generalize the Kuratowski closure-complement problem in special sense. In this paper, we will show that if any pair of operations among closure, interior, boundary and complementations be chosen, then by using only two of the operations on any given set X we obtain that X belongs to a specific finite family. In addition, for any pair of these operations we will give necessary and sufficient condition that the related family puses the largest cardinal number.
Page(s):
1-9
DOI:
DOI not available
Published:
Journal: Punjab University Journal of Mathematics, Volume: 28, Issue: , Year: 1995