Convergence Structures and Applications to Functional Analysis

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This text offers an introduction to the theory and methods of convergence spaces and provides concrete applications to the problems of functional analysis. It highlights the role of continuous convergence, a convergence structure particularly appropriate to function spaces, and demonstrates that it provides an excellent dual structure for both topological groups and topological vector spaces. This text should be of interest to researchers in functional analysis, analysis and topology as well as anyone already working with convergence spaces. It is appropriate for senior undergraduate or graduate level students with some background in analysis and topology.