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Köthe's example of an incomplete LB-space


Authors: J. Kucera and K. McKennon
Journal: Proc. Amer. Math. Soc. 93 (1985), 79-80
MSC: Primary 46A12; Secondary 46M40
DOI: https://doi.org/10.1090/S0002-9939-1985-0766531-1
MathSciNet review: 766531
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Abstract: The inductive limit of reflexive Banach spaces is fast complete. But the inductive limit of reflexive Fréchet spaces may not be fast complete. Also, an example of a complete, reflexive, nuclear space with a quotient space which is not fast complete is given.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0766531-1
Keywords: LB-space, LF-space, completeness, fast completeness
Article copyright: © Copyright 1985 American Mathematical Society

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