Separation Axioms Preserved under Homeomorphism

Theorem
The separation axioms are preserved under homeomorphism.

Let $T_A = \left({X_A, \vartheta_A}\right), T_B = \left({X_B, \vartheta_B}\right)$ be topological spaces.

Let $\phi: T_A \to T_B$ be a homeomorphism.

Then: