Original Articles

SUBSPACES OF BARRELLED SPACES

Published in: Quaestiones Mathematicae
Volume 4, issue 4, 1981 , pages: 323–324
DOI: 10.1080/16073606.1981.9632252
Author(s): JH WebbDepartment of Mathematics, South Africa
Keywords: 46A07

Abstract

Dieudoné [1] showed that finite-codimensional subspace of a barreled locally convex space is itself barreled, and a simple proof was obtained by Komura [2]. The result was later extended to conutable-condimensional subspaces by Saxon and Levin [3] and Valdivia [4]. Their proofs were rather complicated, and in this note we present a simple proof that a countable-codimensional subspace of a barreled space is barrelled.

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