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Topological analysis consists of those basic theorems of analysis which are essentially topological in character, developed and proved entirely by topological and pseudotopological methods. The objective of this volume is the promotion, encouragement, and stimulation of the interaction between topology and analysis-to the benefit of both. Originally published in 1964. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.