Common Definitions
There are several common (and equivalent) definitions to the boundary of a subset S of a topological space X:
- the closure of S without the interior of S: ∂S = S \ So.
- the intersection of the closure of S with the closure of its complement: ∂S = S ∩ (X \ S).
- the set of points p of X such that every neighborhood of p contains at least one point of S and at least one point not of S.
Read more about this topic: Boundary (topology)
Famous quotes containing the words common and/or definitions:
“A country is strong which consists of wealthy families, every member of whom is interested in defending a common treasure; it is weak when composed of scattered individuals, to whom it matters little whether they obey seven or one, a Russian or a Corsican, so long as each keeps his own plot of land, blind in their wretched egotism, to the fact that the day is coming when this too will be torn from them.”
—Honoré De Balzac (1799–1850)
“The loosening, for some people, of rigid role definitions for men and women has shown that dads can be great at calming babies—if they take the time and make the effort to learn how. It’s that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.”
—Pamela Patrick Novotny (20th century)