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Real variables with basic metric space topology. (English) Zbl 0920.26002
New York, NY: IEEE Press. xviii, 213 p. (1993).
From the preface: “This is a text for a first course in real variables. Standard mathematical writing, with its emphasis on formalism and abstraction, tends to create barriers to learning and focus on minor technical details at the expense of intuition. On the other hand, a certain amount of abstraction is unavoidable if one is to give a sound and coherent presentation. This book attempts to strike a balance that will reach the widest audience possible without sacrificing precision.”
Chapter headings: 1. Introduction; 2. Some basic topological properties of \({\mathbb{R}}^p\); 3. Upper and lower limits of sequences of real numbers; 4. Continuous functions; 5. Differentiation; 6. Riemann-Stieltjes integration; 7. Uniform convergence and applications; 8. Further topological results; 9. Epilogue.

26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions