# Tychonoff theorem

### From Conservapedia

**Tychonoff's theorem** states that the product of arbitrary collection of compact topological spaces is compact. Tychonoff's theorem is equivalent to the axiom of choice, and can be proved using transfinite induction.

Stated another way, **Tychonoff's theorem** holds that a nonempty product space is compact if and only if each factor space is compact.