Compactness Properties Preserved under Continuous Surjection

Theorem
Let $T_A = \strict {S_A, \tau_A}$ and $T_B = \strict {S_B, \tau_B}$ be topological spaces.

Let $\phi: T_A \to T_B$ be a continuous surjection.

If $T_A$ has one of the following properties, then $T_B$ has the same property:


 * Compact Space
 * $\sigma$-Compact Space
 * Countable Compact Space
 * Sequential Compact Space
 * Lindelöf Space