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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Every countable-codimensional subspace of a barrelled space is barrelled


Authors: Stephen Saxon and Mark Levin
Journal: Proc. Amer. Math. Soc. 29 (1971), 91-96
MSC: Primary 46.01
MathSciNet review: 0280972
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Abstract: As indicated by the title, the main result of this paper is a straightforward generalization of the following two theorems by J. Dieudonné and by I. Amemiya and Y. Kōmura, respectively:

(i) Every finite-codimensional subspace of a barrelled space is barrelled.

(ii) Every countable-codimensional subspace of a metrizable barrelled space is barrelled.

The result strengthens two theorems by G. Köthe based on (i) and (ii), and provides examples of spaces satisfying the hypothesis of a theorem by S. Saxon.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0280972-0
PII: S 0002-9939(1971)0280972-0
Keywords: Locally convex space, barrelled space, Pták space, Mackey space with property (S), algebraic property of countable-codimensionality, strongest locally convex topology, the bipolar theorem, a perturbation theorem, Schauder basis, positive cone, closed and bounded base
Article copyright: © Copyright 1971 American Mathematical Society