Support of a map

The support $s u p p (𝑓)$ of a real-valued function $𝑓 : 𝑋 \to ℝ$ is the set of all $𝑥 \in 𝑋$ mapped to zero, #m/def/anal i.e.

s u p p (𝑓) = {𝑥 \in 𝑋 : 𝑓 (𝑥) \neq 0}

if $𝑋$ is a topological space the closed support $c l s u p p (𝑓)$ , also called the support is the closure of the support defined above.

Further terminology

A function is said to have compact support iff the closed support is compact.

#state/tidy | #lang/en | #SemBr