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. Kömura, 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. Introduction.N. Bourbaki [2] observed that if £ is a separable, infinite-dimensional Banach space, then E contains a dense subspace M of countably infinite codimension which is a Baire space. R. E. Edwards [4] noted that since M is Baire, it is an example of a noncomplete normed space which is barrelled. Obviously, (i) and (ii) provide a plethora of such examples. It is apparently unknown whether every countable-(or even finite-) codimensional subspace of an arbitrary Baire space is Baire; (for closed subspaces the results are affirmative).In the second paper [8], which follows, the authors give topological properties other than "barrelledness" which are inherited by subspaces having the algebraic property of countable-codimensionality.

No abstract

No abstract

No abstract

No abstract

Abstract.A locally convex space E is said to be ¡¿-barrelled if every countable weak* bounded subset of its topological dual E' is equicontinuous; to have property (C) if every weak* bounded subset of E' is relatively weak* compact; to have property (S) if E' is weak* sequentially complete. If a locally convex space possesses any of the above properties, then so do all of its linear subspaces of countable codimension. Examples are furnished to show that the mentioned properties are distinct from each other.In [4], the authors proved that a linear subspace of countable codimension in a barrelled space is barrelled. In this paper, we see that the properties of a space being w-barrelled and having weak*-sequentially complete dual are inherited by subspaces of countable codimension. Only a partial result is obtained concerning the seemingly most important property, that of being a Mackey space. The paper concludes with examples to demonstrate that the various concepts discussed are, in fact, disjoint.

No abstract

No abstract