A Note on Certain Subalgebras of C()

Abstract

Let be a completely regular Hausdorff space and C( ) the algebra of continuous real-valued functions on . In attempts to characterize abstractly those algebras that are isomorphic to C( ) for some , one produces subalgebras of C( ) which: (a) contain the constant functions, (b) separate points and closed sets in , (c) are closed under uniform convergence, and (d) are closed under inversion in C( ) (see, for example, ( 2 ; 5 )).