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In mathematics, a bump function is a function f : R n → R {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } on a Euclidean space R n {\displaystyle \mathbb {R} ^{n}} which is both smooth and compactly supported. The set of all bump functions with domain R n {\displaystyle \mathbb {R} ^{n}} forms a vector space, denoted C 0 ∞ {\displaystyle C_{0}^{\infty }} or C c ∞ . {\displaystyle C_{c}^{\infty }.} The dual space of this space endowed with a suitable topology is the space of distributions.