Real Variables with Basic Metric Space Topology

Real Variables with Basic Metric Space TopologyDesigned for a first course in real variables, this text presents the fundamentals for more advanced mathematical work, particularly in the areas of complex variables, measure theory, differential equations, functional analysis, and probability. Geared toward advanced undergraduate and graduate students of mathematics, it is also appropriate for students of engineering, physics, and economics who seek an understanding of real analysis. The author

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In later chapters the author introduces vectors and shows how to use vectors and matrices to solve systems of linear equations

and classical Banach and Frechét spaces

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Gerhard Gentzen invented proof-theoretic semantics in the early 1930s

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introducing the functor Ext and exploring the various projective dimensions

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