In a preceding entry of this blog, we saw that topologies arise from closure operators. This note raises the question of whether this is also valid for interior operators. The question is framed precisely in the exercise below. To approach the issue with serenity, it should be remembered here that closure and interior are dual concepts.
Exercise.
Let be a set. If
is an operator which carries subsets of
into subsets of
, and
the family of all subsets such that
, under what conditions will
define a topology on
and
be the interior operator relative to this topology?
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