Analysis MOC

Support of a map

The support supp(𝑓) of a real-valued function 𝑓 :𝑋 →ℝ is the set of all 𝑥 ∈𝑋 mapped to zero, anal i.e.

supp(𝑓)={𝑥∈𝑋:𝑓(𝑥)≠0}

if 𝑋 is a topological space the closed support clsupp(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.

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