Notes for Math 7338

                                Below are some notes about various topics. There is no claim
                                           to originality and some of them follow the book EMT verbatim.


                                          Prologue about limits

                                           Complete metric spaces and contractions

                                           Banach spaces

                                           The Banach limit

                                           Zorn's lemma

                                           Proof of the Hahn Banach Theorem (real case)

                                           The Theorem of Arzelá and Ascoli

                                            Compact operators on a separable Hilbert space

                                           The min-max and max-min principles

                                           The Weierstrass Approximation Theorem

                                           Some notes about semi-continuity

                                           Geometric consequences of the Hahn-Banach theorem