The interior operator o is dual to the closure operator —, in the sense that
- So = X \ (X \ S)—,
and also
- S— = X \ (X \ S)o
where X is the topological space containing S, and the backslash refers to the set-theoretic difference.
Therefore, the abstract theory of closure operators and the Kuratowski closure axioms can be easily translated into the language of interior operators, by replacing sets with their complements.
Read more about this topic: Interior (topology)
Famous quotes containing the word interior:
“Anyone with a real taste for solitude who indulges that taste encounters the dangers of any other drug-taker. The habit grows. You become an addict.... Absorbed in the visions of solitude, human beings are only interruptions. What voice can equal the voices of solitude? What sights equal the movement of a single day’s tide of light across the floor boards of one room? What drama be as continuously absorbing as the interior one?”
—Jessamyn West (1902–1984)