SUBSPACES OF BARRELLED SPACES

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.