A projective description of the space of holomorphic germs (Q2747930)

For a compact set \(K\) in a complex Fréchet space denote by \({\mathcal O}(K)\) the space of germs of holomorphic functions on \(K\). Usually \({\mathcal O}(K)\) is endowed with the inductive topology with respect to all restriction maps \({\mathcal O}(\Omega)\to{\mathcal O}(K)\), where \(\Omega\) runs through all open neighborhoods of \(K\) and where \({\mathcal O}(\Omega)\) carries the compact-open topology. As main result the author shows that this topology can be described by an explicit system of semi-norms which are of Whitney type in the sense that are defined using the Taylor expansion as well as the Taylor remainders. The latter ones are not needed if \(K\) is locally connected. The results extend previous work of Mujica and of Rusek.