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:
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—Abraham Lincoln (1809–1865)
“The rebel can never find peace. He knows what is good and, despite himself, does evil. The value which supports him is never given to him once and for all—he must fight to uphold it, unceasingly.”
—Albert Camus (1913–1960)