Every countable-codimensional subspace of a barrelled space is barrelled

Saxon, Stephen; Levin, Mark

doi:10.1090/S0002-9939-1971-0280972-0

Every countable-codimensional subspace of a barrelled space is barrelled
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by Stephen Saxon and Mark Levin

Proc. Amer. Math. Soc. 29 (1971), 91-96

DOI: https://doi.org/10.1090/S0002-9939-1971-0280972-0

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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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