I was looking at this website:
https://people.math.osu.edu/fiedorowicz.1/math655/Jordan.html
Which had written in it that the Jordan Curve Theorem for C^1 simple closed curves was easy to prove.
I'm looking for advice on how one might go about proveing this restricted version of the theorem?
I was able to create two open sets as follows: using the fact I can create a perpendicular line from a point on the curve I could then choose a point on each side of the curve and then use open sets to create an open covering on each side of the curve.
The problem is I don't know how I would go about showing the two sets are disjoint.
Any advice would be very helpfull.