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Extendibility,
boundedness and sequential convergence in spaces of
holomorphic functions
William Robin Zame |
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Vol. 57 (1975), No. 2, 619–628
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Abstract |
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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
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Milestones
Received: 22 August 1974
Published: 1 April 1975
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Authors |
| William Robin Zame | |
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