I have currently been studying space of continuous functions from J.B. Conway's textbook of complex variable. In Chapter VII of the textbook, it uses the notation $C(G,S)$ to denote the space of all continuous functions from open set $G$ to $S$
WHERE $(S,d)$ is a complete metric space.
Why is it taking the space $(S,d)$ to be complete metric space. What would happen if we take any arbitrary metric space? or is it necessary to take $(S,d)$ complete?