Continuous Functions On A Compact Hausdorff Space
In mathematical analysis, and especially functional analysis, a fundamental role is played by the space of continuous functions on a compact Hausdorff space with values in the real or complex numbers. This space, denoted by C(X), 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
the uniform norm. The uniform norm defines the topology of uniform convergence of functions on X. The space C(X) is a Banach algebra with respect to this norm. (Rudin 1973, ยง11.3)
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