Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Dense barrelled subspaces of uncountable codimension
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by Stephen A. Saxon and Wendy J. Robertson
Proc. Amer. Math. Soc. 107 (1989), 1021-1029
DOI: https://doi.org/10.1090/S0002-9939-1989-0990433-2

Abstract:

Let $E$ be a Hausdorff barrelled space. If there exists a dense barrelled subspace $M$ such that $(\operatorname {codim} (M) \geq c)[\operatorname {codim} (M) = \operatorname {dim} (E)]$, we say that ($M$ is a satisfactory subspace [11]) [$E$ is barrelledly fit], respectively. Robertson, Tweddle and Yeomans [11] proved that $E$ has a barrelled countable enlargement (BCE) if it has a satisfactory subspace. (Trivially) $E$ has a satisfactory subspace if $\dim (E) \geq c$ and $E$ is barrelledly fit. We show that $E$ is barrelledly fit (and $\dim (E) \geq c$) if $E \ncong \varphi$ and either (i) $E$ is an (LF)-space, or (ii) $E$ is an infinite-dimensional separable space and the continuum hypothesis holds. Conclusion: barrelledly fit spaces and their permanence properties arise from and advance the study of BCE’s.
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Bibliographic Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 1021-1029
  • MSC: Primary 46A07
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0990433-2
  • MathSciNet review: 990433