  Spherically complete ball spaces provide a framework for the proof of generic
fixed point theorems. For the purpose of their application it is important to
have methods for the construction of new spherically complete ball spaces from
given ones. Given various ball spaces on the same underlying set, we discuss
the construction of new ball spaces through set theoretic operations on the
balls. A definition of continuity for functions on ball spaces leads to the
notion of quotient spaces. Further, we show the existence of products and
coproducts and use this to derive a topological category associated with ball
spaces.
