Are Jordan Domains Locally Connected?

Question

I have been trying to answer this question, to which I do not know the answer. Are Jordan Domains locally connected?

In this context, a Jordan Domain is just the bounded interior of a Jordan curve.

Edit: In fact, I know the answer. It is true due to the Caratheodory Extension theorem. However, could it be proven using exclusively topological arguments?

Answer 1

Yes. The bounded interior is actually homeomorphic to an open ball, by the Schönflies Theorem. Hence it is locally connected. The closure is also locally connected, being homeomorphic to a closed disc, by the same theorem.