On the size of quotients of function spaces on a topological group
For a non-precompact topological group G, we consider the space C(G) of bounded, continuous, scalar-valued functions on G with the supremum norm, together with the subspace LMC(G) of left multiplicatively continuous functions, the subspace LUC(G) of left norm continuous functions, and the subspace WAP(G) of weakly almost periodic functions. We establish that the quotient space LUC(G)/WAP(G) contains a linear isometric copy of , and that the quotient space C(G)/LMC(G) (and a fortiori C(G)/LUC(G))...