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:
“I am reminded by my journey how exceedingly new this country still is. You have only to travel for a few days into the interior and back parts even of many of the old States, to come to that very America which the Northmen, and Cabot, and Gosnold, and Smith, and Raleigh visited.”
—Henry David Thoreau (1817–1862)