Closed Supports
The most common situation occurs when X is a topological space (such as the real line) and f : X→R is a continuous function. In this case, only closed supports of X are considered. So a (topological) support of f is a closed subset of X outside of which f vanishes. In this sense, supp(f ) is the intersection of all closed supports, since the intersection of closed sets is closed. The topological supp(f ) is the topological closure of the set-theoretic supp(f ).
Read more about this topic: Support (mathematics)
Famous quotes containing the words closed and/or supports:
“Don: Why are they closed? They’re all closed, every one of them.
Pawnbroker: Sure they are. It’s Yom Kippur.
Don: It’s what?
Pawnbroker: It’s Yom Kippur, a Jewish holiday.
Don: It is? So what about Kelly’s and Gallagher’s?
Pawnbroker: They’re closed, too. We’ve got an agreement. They keep closed on Yom Kippur and we don’t open on St. Patrick’s.”
—Billy Wilder (b. 1906)
“The tendency of the casual mind is to pick out or stumble upon a sample which supports or defies its prejudices, and then to make it the representative of a whole class.”
—Walter Lippmann (1889–1974)