 Space of holomorphic functions (source code)

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= Space of holomorphic functions
{title2=$\mathcal O(U)$}

For an <open set> $U\subseteq\mathbb C$, the space $\mathcal O(U)$ consists of all <holomorphic function>[holomorphic functions] on $U$. Its standard topology is locally uniform convergence, equivalently the <compact-open topology> defined by the seminorms $f\mapsto\sup_{z\in K}|f(z)|$ for compact $K\subset U$.

= Analytic function
{synonym}

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