Support of a function

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defined on a topological space

The smallest closed set such that the values of the numerical function are zero everywhere on the complement . In other words, is the closure of the set of all points for which .


A function is said to be of compact support if is compact. The functions of compact support with values in , or (or other rings or fields), form a vector space.


[a1] W. Rudin, "Real and complex analysis" , McGraw-Hill (1966) pp. 38
How to Cite This Entry:
Support of a function. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article