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In mathematical analysis, and especially functional analysis, a fundamental role is played by the space of continuous functions on a compact Hausdorff space X {\displaystyle X} with values in the real or complex numbers. This space, denoted by C , {\displaystyle {\mathcal {C}},} is a vector space with respect to the pointwise addition of functions and scalar multiplication by constants. It is, moreover, a normed space with norm defined by

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