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:
“Nobody can deny but religion is a comfort to the distressed, a cordial to the sick, and sometimes a restraint on the wicked; therefore whoever would argue or laugh it out of the world without giving some equivalent for it ought to be treated as a common enemy.”
—Mary Wortley, Lady Montagu (1689–1762)
“Lord Byron is an exceedingly interesting person, and as such is it not to be regretted that he is a slave to the vilest and most vulgar prejudices, and as mad as the winds?
There have been many definitions of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.”
—Edmond De Goncourt (1822–1896)