Completely regular space

Definition
A topological space is termed completely regular if it satisfies the following equivalent conditions:

Convention issues
Note that in some conventions, the $$T_1$$ assumption is made along with completely regular. We use the term Tychonoff space here for a completely regular space that is also $$T_1$$.

Textbook references

 * , Page 211, Chapter 4, Section 33 (formal definition)
 * , Page 37 (formal definition)