Alexander's trick and homeomorphism extension

It is quite well known fact that if f:S^1 -> S^1
is an orientation-preserving homeomorphism,
then it can be extended to an orientation
preserving homeomorphism of the closed unit
disk bar{D}, and the extension is unique up to
isotopy rel S^1.

Could there be any analogous statement in case
i have a topological disk U in C, but it's
boundary might not be Jordan ?

any counter-examles?

Thanks.


Message was edited by: jane

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