Characterization of C(x) among its Subalgebras

Unit ball Banach-Algebra Hold Hahn-Banach Theorem Complex Variables Compact set Closed graph theorem Follow Dense Banach algebra norm Closed Convex Hull Closed Subsets Compact Subsets Compact Neighborhood Disjoint Closed Subsets Closed Unit Ball Commutative Banach Algebra Compact Hausdorff Space Continuous Complex Function E Lies Linear Space Norm Old-about subalgebras Open Map Theorem Quotient Norm Normed Algebra Prototypical Weierstrass approximation theory Open Neighborhood Quotient algebra Uniformly Closed