On α-Cogenerated Commutative Unital C*-Algebras

الملخص EN

Gelfand-Naimark's theorem states that every commutative C*-algebra is isomorphic to a complex valued algebra of continuous functions over a suitable compact space.

We observe that for a completely regular space X, βX is dense-α-separable if and only if C(X) is α-cogenerated if and only if every family of maximal ideals of C(X) with zero intersection has a subfamily with cardinal number less than α and zero intersection.

This gives a simple characterization of α-cogenerated commutative unital C*-algebras via their maximal ideals.