On the Functionally Countable Subalgebra of $C(X)$
On the Functionally Countable Subalgebra of $C(X)$
Let {C_c{{\char 40}}X{{\char 41}}} =\{\,f\in C(X): f(X) \hbox{ is countable}\} . Similar to C(X) it is observed that the sum of any collection of semiprime (resp. prime) ideals in the ring {C_c{{\char 40}}X{{\char 41}}} is either {C_c{{\char 40}}X{{\char 41}}} or a semiprime (resp. prime) ideal in {C_c{{\char 40}}X{{\char 41}}} . …