In Segal's paper on $\Gamma$-spaces, he gives a functor $Spectra \rightarrow \Gamma-Spaces$ defined by taking a functor $E$ and sending it to the $\Gamma$-space $AE$ with $AE(n) = Mor(S \times \cdots \times S, E)$, where $S$ is the sphere spectrum. Now, since this is supposed to define a $\Gamma$-space, in particular the sets $Mor(S \times \cdots \times S, E)$ should be topological spaces... but they don't seem to come with any obvious topology, at least not obvious to me.

On the other hand, it seems like there should be some sort of spectrum that acts like $Mor(S \times \cdots \times S, E)$; could he mean, possibly, the 0th space of this spectrum?

EDIT: The reference is

Segal, Graeme Categories and cohomology theories. Topology 13 (1974), 293--312