Page "Holomorphic function" Paragraph 7

If ƒ is complex differentiable at every point z < sub > 0 </ sub > in an open set U, we say that ƒ is holomorphic on U. We say that ƒ is holomorphic at the point z < sub > 0 </ sub > if it is holomorphic on some neighborhood of z < sub > 0 </ sub >.

We say that ƒ is holomorphic on some non-open set A if it is holomorphic in an open set containing A.