: Mathematics: bump function

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bump function

In mathematics, a bump function (also called a test function) is a function ${\\displaystyle f:\\mathbb {R} ^{n}\ o \\mathbb {R} }$ on a Euclidean space ${\\displaystyle \\mathbb {R} ^{n}}$ which is both smooth (in the sense of having continuous derivatives of all orders) and compactly supported. The set of all bump functions with domain ${\\displaystyle \\mathbb {R} ^{n}}$ forms a vector space, denoted ${\\displaystyle \\mathrm {C} _{0}^{\\infty }(\\mathbb {R} ^{n})}$ or ${\\displaystyle \\mathrm {C} _{\\mathrm {c} }^{\\infty }(\\mathbb {R} ^{n}).}$ The dual space of this space endowed with a suitable topology is the space of distributions.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Bump_function)

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