Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses.

9. Metric Spaces: General Properties.

• 9.1. Examples of Metric Spaces. Section 9.1 notes
• 9.2. Open Sets, Closed Sets, and Convergent Sequences. Section 9.2 notes
• Supplement. Proofs of Theorems in Section 9.2. Beamer file of Section 9.2 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 9.2. Beamer file of Section 9.2 proofs
• 9.3. Continuous Mappings Between Metric Spaces. Section 9.3 notes
• Supplement. Proofs of Theorems in Section 9.3. Beamer file of Section 9.3 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 9.3. Beamer file of Section 9.3 proofs
• 9.4. Complete Metric Spaces. Section 9.4 notes
• Supplement. Proofs of Theorems in Section 9.4. Beamer file of Section 9.4 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 9.4. Beamer file of Section 9.4 proofs
• 9.5. Compact Metric Spaces. Section 9.5 notes
• Supplement. Proofs of Theorems in Section 9.5. Beamer file of Section 9.5 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 9.5. Beamer file of Section 9.5 proofs
• 9.6. Separable Metric Spaces. Section 9.6 notes
• Supplement. Proofs of Theorems in Section 9.6. Beamer file of Section 9.6 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 9.6. Beamer file of Section 9.6 proofs
• Study Guide 9.

10. Metric Spaces: Three Fundamental Theorems.

• 10.1. The Arzelà-Ascoli Theorem. Section 10.1 notes
• Supplement. Proofs of Theorems in Section 10.1. Beamer file of Section 10.1 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 10.1. Beamer file of Section 10.1 proofs
• 10.2. The Baire Category Theorem. Section 10.2 notes (Contains some biographical information on René Baire.)
• Supplement. Proofs of Theorems in Section 10.2. Beamer file of Section 10.2 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 10.2. Beamer file of Section 10.2 proofs
• 10.3. The Banach Contraction Principle. Section 10.3 notes
• Supplement. Proofs of Theorems in Section 10.3. Beamer file of Section 10.3 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 10.3. Beamer file of Section 10.3 proofs
• Study Guide 10.

11. Topological Spaces: General Properties.

• 11.1. Open Sets, Closed Sets, Bases, and Subbases. Section 11.1 notes
• Supplement. Proofs of Theorems in Section 11.1. Beamer file of Section 11.1 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 11.1. Beamer file of Section 11.1 proofs
• 11.2. The Separation Properties. Section 11.2 notes
• Supplement. Proofs of Theorems in Section 11.2. Beamer file of Section 11.2 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 11.2. Beamer file of Section 11.2 proofs
• 11.3. Countability and Separability. Section 11.3 notes
• Supplement. Proofs of Theorems in Section 11.3. Beamer file of Section 11.3 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 11.3. Beamer file of Section 11.3 proofs
• 11.4. Continuous Mappings Between Topological Spaces. Section 11.4 notes
• Supplement. Proofs of Theorems in Section 11.4. Beamer file of Section 11.4 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 11.4. Beamer file of Section 11.4 proofs
• 11.5. Compact Topological Spaces. Section 11.5 notes
• Supplement. Proofs of Theorems in Section 11.5. Beamer file of Section 11.5 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 11.5. Beamer file of Section 11.5 proofs
• 11.6. Connected Topological Spaces. Section 11.6 notes
• Supplement. Proofs of Theorems in Section 11.6. Beamer file of Section 11.6 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 11.6. Beamer file of Section 11.6 proofs
• Study Guide 11.

12. Topological Spaces: Three Fundamental Theorems.

• 12.1. Urysohn's Lemma and The Tietze Extension Theorem. Section 12.1 notes
• Supplement. Proofs of Theorems in Section 12.1. Beamer file of Section 12.1 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 12.1. Beamer file of Section 12.1 proofs
• 12.2. The Tychonoff Product Theorem. Section 12.2 notes
• Supplement. Proofs of Theorems in Section 12.2. Beamer file of Section 12.2 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 12.2. Beamer file of Section 12.2 proofs
• 12.3. The Stone-Weierstrass Theorem. Section 12.3 notes
• Supplement. Proofs of Theorems in Section 12.3. Beamer file of Section 12.3 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 12.3. Beamer file of Section 12.3 proofs
• Study Guide 12.

13. Continuous Linear Operators Between Banach Spaces.

• 13.1. Normed Linear Spaces. Section 13.1 notes
• 13.2. Linear Operators. Section 13.2 notes
• Supplement. Proofs of Theorems in Section 13.2. Beamer file of Section 13.2 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 13.2. Beamer file of Section 13.2 proofs
• 13.3. Compactness Lost: Infinite Dimensional Normed Linear Spaces. Section 13.3 notes
• Supplement. Proofs of Theorems in Section 13.3. Beamer file of Section 13.3 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 13.3. Beamer file of Section 13.3 proofs
• 13.4. The Open Mapping and Closed Graph Theorems.
• 13.5. The Uniform Boundedness Principle.
• Study Guide 13.

14. Duality for Normed Linear Spaces.

• 14.1. Linear Functionals, Bounded Linear Functionals, and Weak Topologies. Section 14.1 notes
• Supplement. Proofs of Theorems in Section 14.1. Beamer file of Section 14.1 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 14.1. Beamer file of Section 14.1 proofs
• 14.2. The Hahn-Banach Theorem. Section 14.2 notes
• Supplement. Proofs of Theorems in Section 14.2. Beamer file of Section 14.2 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 14.2. Beamer file of Section 14.2 proofs
• 14.3. Reflexive Banach Spaces and Weak Sequential Convergence.
• 14.4. Locally Convex Topological Vector Spaces.
• 14.5. The Separation of Convex Sets and Mazur's Theorem.
• 14.6. The Krein-Milman Theorem.
• Study Guide 14.

15. Compactness Regained: The Weak Topology.

• 15.1. Alaoglu's Extension of Helley's Theorem.
• 15.2. Reflexivity and Weak Compactness: Kakutani's Theorem.
• 15.3. Compactness and Weak Sequential Compactness: The Eberlein-Smulina Theorem.
• 15.4. Metrizability of Weak Topologies.
• Study Guide 15.

16. Continuous Linear Operators on Hilbert Spaces.

• 16.1. The Inner Product and Orthogonality. Section 16.1 notes
• Supplement. Proofs of Theorems in Section 16.1. Beamer file of Section 16.1 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 16.1. Beamer file of Section 16.1 proofs
• 16.2. The Dual Space and Weak Sequential Convergence. Section 16.2 notes
• Supplement. Proofs of Theorems in Section 16.2. Beamer file of Section 16.2 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 16.2. Beamer file of Section 16.2 proofs
• 16.3. Bessel's Inequality and Orthonormal Bases. Section 16.3 notes
• Supplement. Proofs of Theorems in Section 16.3. Beamer file of Section 16.3 proofs (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 16.3. Beamer file of Section 16.3 proofs
• 16.4. Adjoints and Symmetry for Linear Operators.
• 16.5. Compact Operators.
• 16.6. The Hilbert-Schmidt Theorem.
• 16.7. The Riesz-Schauder Theorem: Characterization of Fredholm Operators.
• Study Guide 17.

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