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:
“We are closed in, and the key is turned
On our uncertainty;”
—William Butler Yeats (1865–1939)
“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)