# Talk:Domain of holomorphy

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## Is there an inverse?

The statement "we can define a holomorphic function with zeros accumulating everywhere on the boundary of the domain, which must then be a natural boundary for a domain of definition of its inverse" looks strange, since the function is not injective and so does not have an inverse. --Stomatapoll (talk) 04:21, 25 March 2015 (UTC)

I think what's meant is that the reciprocal function ${\displaystyle g(z)={\frac {1}{f(z)}}}$ cannot be extended beyond ${\displaystyle \Omega }$, since it has a dense set of singularities on the boundary. I'll replace inverse with reciprocal to make it clearer.--71.205.130.248 (talk) 21:09, 7 September 2016 (UTC)