Local Compactness is Preserved under Open Continuous Surjection

Theorem
Let $T_A = \left({S_A, \tau_A}\right)$ and $T_B = \left({S_B, \tau_B}\right)$ be topological spaces.

Let $\phi: T_A \to T_B$ be a continuous mapping which is also an open mapping and a surjection.

If $T_A$ is locally compact, then $T_B$ is also locally compact.

Also see

 * Weak Local Compactness is Preserved under Open Continuous Surjection