Pairings of function spaces (Q2371791)

Pairings \(\mu :X\times Y\rightarrow Z\) and copairings \(\theta :A\rightarrow B\) \(\vee \) \(C\) induce pairings in homotopy sets \(\mu _{\ast }:[A,X]\times [A,Y]\rightarrow [ A,Z]\) and \(\theta ^{\ast }:[B,Z]\times [C,Z]\rightarrow [ A,Z]\). This paper constructs pairings at the level of function spaces for these pairings in homotopy sets. The crucial point is finding a correct choice of topologies for the function spaces.