Definition 27.2.4 (Space of Holomorphic Functions Near a Set).label Let $E$ be a complete separated locally convex space over $\complex$ and $A \subset \complex$. Direct $\cn_{\complex}^{o}(A)$ under reverse inclusion, then the inductive limit
\[H(A; E) = \varinjlim_{U \in \cn_{\complex}^o(A)}H(U; E)\]
is the space of holomorphic functions near $A$, and is of type (LF).
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