# Support of a function

From Encyclopedia of Mathematics

* 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 .

#### Comments

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.

#### References

[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: http://encyclopediaofmath.org/index.php?title=Support_of_a_function&oldid=14245

This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article