On the stability of barrelled topologies, III

Author:

Robertson W.J.,Tweddle I.,Yeomans F.E.

Abstract

Let E be a barrelled space with dual FE*. It is shown that F has uncountable codimension in E*. If M is a vector subspace of E* of countable dimension with MF = {o}, the topology τ(E, F+M) is called a countable enlargement of τ(E, F). The results of the two previous papers are extended: it is proved that a non-barrelled countable enlargement always exists, and sufficient conditions for the existence of a barrelled countable enlargement are established, to include cases where the bounded sets may all be finite dimensional. An example of this case is given, derived from Amemiya and Kōmura; some specific and general classes of spaces containing a dense barrelled vector subspace of codimension greater than or equal to c are discussed.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

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