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    Supremum Norm

    Definition

    Let K be a T_2-topological space and let F be the space of all bounded complex-valued continuous functions defined on K. The supremum norm is the norm defined on F by left double bracketing bar f right double bracketing bar = sup_(x element K) left bracketing bar f(x) right bracketing bar . Then F is a commutative Banach algebra with identity.

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