On Q, QM and QM#-algebras

The concepts of QM and QM#-algebras were defined in [4] as generalizations of Q-algebras. In this paper we prove that, if X is a completely regular Hausdorff space, then the uniform topology σ is the only topology τ on Cb (X) which is coarser than σ and possesses the following property: A = (Cb (X), τ) is a topological algebra and the above three concepts are equivalent for A. We also construct a B0-algebra which is a QM-algebra, but it is not a Q-algebra.