In the theory of locally convex topological vector spaces, barrelled topologies have been found to be stable under the formation of products, sums and quotients. We shall in this thesis investigate the stability of barrelled topologies with respect to two further mathematical constructions. Firstly, we examine the situation with regard to the formation of finite-codimensional and countable-codimensional subspaces. (Of course, barrelled topologies are not stable under the formation of arbitrary subspaces.) Secondly, we present what is known about the stability of barrelled topologies with respect to enlargements of the dual space - a concept which is defined in the sequel. This aspect of the stability question was tackled in a recent paper by Robertson and Yeomans and was pursued in two subsequent papers by Tweddle and Yeomans and by Robertson, Tweddle and Yeomans. In the next two chapters, we turn our attention to quasibarrelled topologies and we pursue a parallel investigation to that of the first two chapters. Finally we conduct a similar investigation on σ-barrelled and σ-quasibarrelled spaces. The results 5.2, 5.3, 5.4, 5.5, 5.6, 6.2, 6.3, 6.4 and 6.5 concerning these spaces are original.

Bibliography: leaf 86-88.