Uniform algebra is a concept from functional analysis, a branch of mathematics that deals with vector spaces and operators on these spaces. More specifically, a uniform algebra is a type of Banach algebra that is defined using certain properties related to uniform convergence.
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A uniform algebra on a compact Hausdorff space is a closed complex subalgebra of , with the supremum norm, containing the constants and separating points. Evaluation embeds continuously and injectively in the character space of an algebra. The embedding is a homeomorphism onto a closed subset because its domain is compact and its target is Hausdorff. Extra characters need not be point evaluations on the specified .