On John domains in Banach spaces

We study the stability of John domains in Banach spaces under removal of a countable set of points. In particular, we prove that the class of John domains is stable in the sense that removing a certain type of closed countable set from the domain yields a new domain which also is a John domain. We apply this result to prove the stability of the inner uniform domains. Finally, we consider a wider class of domains, so called $ψ$-John domains and prove a similar result for this class.

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