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I was looking at this website:

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.

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