Introductory Real Analysis
Self-contained and comprehensive, this elementary introduction to real and functional analysis is readily accessible to those with background in advanced calculus. It covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, and much more. 350 problems. 1970 edition.
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I have read this book from its German translation. That was more understandable. Its English version is like you read and read and read but it's all trivial. You can't get at the point.