Hi, is there something like : $X^{Y \times Z}$ homeomorph to $(X^Y)^Z $ with compact open topologies if and only if "...." with conditions "...." on Z ,Y and maybe X? famous is : Z T2 and Y locally compact => $X^{Y \times Z}$ homeomorph to $(X^Y)^Z $ and you can weak this a bit but not to an equivalence.