I have tried many things but I have not succeeded. I am trying to find a topological proof of the fact that all boundary points of a simply connected, bounded Jordan Domain (i.e, the bounded interior of a Jordan curve) are simple boundary points. Is there some proof that does not use the Caratheodory extension theorem?
The definition of simple boundary point can be found in https://planetmath.org/simpleboundarypoint.
From what I have seen, it would be enough to show that every such Jordan Domain is locally connected. Is that true?