Let BiL(X Y, Z) denote the set of all continuous bilinear functions from X Y

Question:

Let BiL(X × Y, Z) denote the set of all continuous bilinear functions from X × Y to Z. Show that BiL(X × Y, Z) is a linear space.
The following result may seem rather esoteric but is really a straightforward application of earlier definitions and results. It will be used in the next chapter.