Core point-set definitions and four separation/product theorems

State definitions of the following:

1. product topology;
2. normal space;
3. regular space;
4. second-countable space.

Then state:

1. the Tychonoff Product Theorem;
2. Urysohn’s Lemma;
3. the Urysohn Metrization Theorem;
4. the Tietze Extension Theorem.