No abstract

No abstract

The theme of this book is the Structure Theory of compact groups. It contains a completely selfcontained introduction to linear Lie groups and a substantial body of material on compact Lie groups. The authors' approach is distinctive in so far as they define a linear Lie group as a particular subgroup of the multiplicative group of a Banach algebra. Compact Lie groups are recognized at an early stage as being linear Lie groups. This approach avoids the use of machinery on manifolds. The text is written in a style to make it accessible to the beginning graduate student with a basic knowledge in analysis, algebra, and topology. At the same time the expert will find it an excellent and rich source of information on the general structure theory of compact groups.

No abstract

Abstract. We define and study the free topological vector space V(X) over a Tychonoff space X. We prove that V(X) is a kω-space if and only if X is a kω-space. If X is infinite, then V(X) contains a closed vector subspace which is topologically isomorphic to V(N). It is proved that if X is a k-space, then V(X) is locally convex if and only if X is discrete and countable. If X is a metrizable space it is shown that: (1) V(X) has countable tightness if and only if X is separable, and (2) V(X) is a k-space if and only if X is locally compact and separable. It is proved that V(X) is a barrelled topological vector space if and only if X is discrete. This result is applied to free locally convex spaces L(X) over a Tychonoff space X by showing that: (1) L(X) is quasibarrelled if and only if L(X) is barrelled if and only if X is discrete, and (2) L(X) is a Baire space if and only if X is finite.

No abstract

No abstract

No abstract