Vol. 57, No. 2, 1975

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Extendibility, boundedness and sequential convergence in spaces of holomorphic functions

William Robin Zame

Vol. 57 (1975), No. 2, 619–628

Let X be a compact subset of Cm and let p(X) be the space of germs on X of functions holomorphic near X, equipped with its natural locally convex inductive limit topology. The object of this paper is to give, under a mild topological assumption on X, an internal description of this topology, and in particular, of the bounded sets and convergent sequences. These results follow from a general extendibility theorem. Surprisingly, the topological assumption on X is necessary, and examples are constructed which illustrate this point. A related local extendibility result is also established.

Mathematical Subject Classification 2000
Primary: 32D15
Received: 22 August 1974
Published: 1 April 1975
William Robin Zame