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Bounded sets in inductive limits

Authors: J. Kučera and K. McKennon
Journal: Proc. Amer. Math. Soc. 69 (1978), 62-64
MSC: Primary 46M10; Secondary 46A05
MathSciNet review: 0463937
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Abstract: The Dieudonné-Schwartz theorem for bounded sets in strict inductive limits does not hold for general inductive limits. A set B bounded in an inductive limit $ E = {\operatorname{ind}}\;\lim {E_n}$ of locally convex spaces may not be contained in any $ {E_n}$. If, however, each $ {E_n}$ is closed in E, then B is contained in some $ {E_n}$, but may not be bounded there.

References [Enhancements On Off] (What's this?)

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  • [2] John Horváth, Topological vector spaces and distributions. Vol. I, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0205028
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Keywords: Locally convex space, inductive limit, bounded set, finest locally convex topology
Article copyright: © Copyright 1978 American Mathematical Society

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