An illustrative introduction to modern analysis - Katzourakis, Nikolaos; Varvaruca, Eugen; CRC Press (Boca Raton, FL : CRC Press, an imprint of Chapman and Hall/CRC, 2018)
Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis.
chapter 1 Sets, mappings, countability and choice / Nikos Katzourakis -- chapter 2 Metric spaces and normed spaces / Nikos Katzourakis -- chapter 3 Completeness and applications / Nikos Katzourakis -- chapter 4 Topological spaces and continuity / Nikos Katzourakis -- chapter 5 Compactness and sequential compactness / Nikos Katzourakis -- chapter 6 The Lebesgue measure on the Euclidean space / Nikos Katzourakis -- chapter 7 Measure theory on general spaces / Nikos Katzourakis -- chapter 8 The Lebesgue integration theory / Nikos Katzourakis -- chapter 9 The class of Lebesgue functional spaces / Nikos Katzourakis -- chapter 10 Inner Product Spaces and Hilbert Spaces / Nikos Katzourakis -- chapter 11 Linear operators on normed spaces / Nikos Katzourakis -- chapter 12 Weak topologies on Banach Spaces / Nikos Katzourakis -- chapter 13 Weak* topologies and compactness / Nikos Katzourakis -- chapter 14 Functional properties of the Lebesgue spaces / Nikos Katzourakis -- chapter 15 Solutions to the exercises / Nikos Katzourakis.
Keywords: Mathematical analysis -- Textbooks