Suppose V1,…,VmV_1,\dots,V_mV1,…,Vm are vector spaces. Prove that L(V1×⋯×Vm,W)\mathcal L(V_1 \times \dots \times V_m, W)L(V1×⋯×Vm,W) and L(V1,W)×⋯×L(Vm,W)\mathcal L(V_1,W)\times \dots\times \mathcal L(V_m,W)L(V1,W)×⋯×L(Vm,W) are isomorphic vector spaces.
TODO