Abstract
This chapter discusses weakly compact subsets of Banach spaces. The fields of analysis, general topology, and set theory have another happy reunion in the study of weakly compact subsets of Banach spaces. This chapter also presents some of the basic results and recent advances relating to weakly compact sets from a set theoretic topologist's point of view. The EC spaces are topological spaces that are homeomorphic to weakly compact subsets of Banach spaces. EC spaces are preserved under closed subsets, countable products, and continuous images. The concept of an EC space originated in the study of Banach spaces and continues to play an important role in the field. This chapter also reviews a few of the basic Banach space and measure space results concerning ECs and discusses the way in which these results relate to set theoretic topology.
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