Compactness Principles for Topological Vector Spaces

Abstract We show that the many of the canonical quantifications of interrelated concepts, centered around compactness in the setting of metric spaces, can be easily generalized to the setting of topological linear spaces. Among other things, we obtain a generalization of the Hausdorff Total Boundedness Principle, of the Grothendieck Compactness Principle, as well as of the Convex Compactness Principle for topological vector spaces.