Let $(X_1,\tau_1)$ and $(X_2,\tau_2)$ be topological spaces. Prove that $(X_1,\tau_1)\times(X_2,\tau_2)\cong (X_2,\tau_2)\times(X_1,\tau_1) $.
This is a weird exercise once I can visualize there is a swap of the axis between the two spaces which keeps the spaces being homeomorphic. But I cannot conceive a proof of the statement.
Question:
How should I prove the statement?
Thanks in advance!