The term “support” means different things in different parts of mathematics:

In set theory

Given f:XAf \colon X \to A a function to AA a pointed object with the point playing the role of a zero element, then the support of ff is the subobject of XX on which ff is non-zero.

In topology

In topology the support of a continuous function f:XAf \colon X \to A as above is the topological closure of the set of points on which ff does not vanish:

Supp(f)=Cl({xX|f(x)0A}). Supp(f) = Cl(\{x \in X \vert f(x) \neq 0 \in A\}) \,.

If Supp(f)XSupp(f) \subset X is a compact subspace, then one says that ff has compact support.

In functional analysis

In topos theory and type theory

support = (-1)-truncation


Revised on July 28, 2017 05:44:00 by Urs Schreiber (