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:
“Though the railroad and the telegraph have been established on the shores of Maine, the Indian still looks out from her interior mountains over all these to the sea.”
—Henry David Thoreau (1817–1862)