Q:

Where is Van Kampen's theorem about curves and two-sided surfaces?

I am looking for this theorem: 

For any C there is always a smooth two-sided surface which doesn't cross itself, and whose boundary is C

I saw this statement here on page 2 with a note 

This was first proved around 1930 by van Kampen

But I don't find this theorem anywhere. Where is it?

A:

Two-sided embedded surfaces which bound a smooth curve (also called a knot) $C$ are known as Seifert surfaces for the knot. I don't know a precise reference to van Kampen's result but the Wikipedia article seems to disagree he was the first to prove the existence of a Seifert surface for every knot. If you're looking for a proof, there's an algorithm for constructing them, which you can find all over the internet or in any knot theory book.

