Preface to the Series
Preface to Part 1
Chapter 1.Preliminaries
1.1.Notation and Terminology
1.2.Metric Spaces
1.3.The Real Numbers
1.4.Orders
1.5.The Axiom of Choice and Zorn's Lemma
1.6.Countability
1.7.Some Linear Algebra
1.8.Some Calculus
Chapter 2.Topological Spaces
2.1.Lots of Definitions
2.2.Countability and Separation Properties
2.3.Compact Spaces
2.4.The Weierstrass Approximation Theorem and Bernstein Polynomials
2.5.The Stone-Weierstrass Theorem
2.6.Nets
2.7.Product Topologies and Tychonoff's Theorem
2.8.Quotient Topologies
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