- Lecturer
- Alessandro Sisto
- Coordinator
- Davide Spriano

An introduction to topology i.e. the domain of mathematics that studies how to define the notion of continuity on a mathematical structure, and how to use it to study and classify these structures. Topics covered include: Topological and metric spaces, continuity, connectedness, compactness, product spaces, separation axioms, quotient spaces, homotopy, fundamental group, covering spaces.

The first part of the course will follow Allen Hatcher's Notes. If you don't know where to find a proof, you may want to look at Proof Wiki.

The second part of the course will cover the fundamental group of a topological space. The main references are Chapters 9-11-13-14 of the book "Topology" by James Munkres, and the Chapters 0-1 of the book Algebraic Topology of Allen Hatcher.

- 19 February - Introduction
- 21 February - Pages 1-5 ("Interior, Closure, and Boundary" excluded)
- 26 February - Pages 5-7 ("Interior, Closure, and Boundary")
- 28 February - Pages 7-17 (Finished Chapter 1)
- 5 and 7 March - Pages 18-25 (Chapeter 2 up to "The Cantor Set")
- 12 and 14 March - Pages 25-33 ("The Cantor Set" and beginning of Compactness) - List of statements for Lecture 8
- 19 March - Pages 39-41 ("Infinite products") - List of statements for Lecture 9
- 21 March - See Munkres. For precise reference see the List of statements for Lecture 10
- 26 March - Hatcher Pages 38-39 ("Lebesgue Numbers") - List of statements for Lecture 11
- 29 March - Munkres Page 290 (Ascoli's Theorem) - List of statements for Lecture 12
- 9 April - Hatcher Page 35 - List of statements for Lecture 13
- 11 April - Hatcher Page 35-37 - List of statements for Lecture 14
- 16 April - Hatcher Page 44 (Beginning of "Quotient spaces") - List of statements for Lecture 15
- 18 April - Hatcher Page 45-47 (More on "Quotient spaces") - List of statements for Lecture 16
- 23 April - List of statements for Lecture 17
- 25 April - List of statements for Lecture 18

The second part of the course will cover the fundamental group of a topological space. The main references are Chapters 9-11-13-14 of the book "Topology" by James Munkres, and the Chapters 0-1 of the book Algebraic Topology of Allen Hatcher.

- 30 April - List of statements for Lecture 19
- 2 May - List of statements for Lecture 20
- 7 May - List of statements for Lecture 21
- 9 May - List of statements for Lecture 22
- 14 May - List of statements for Lecture 23
- 16 May - List of statements for Lecture 24

Here you can find an updated list of statements for the whole course which also indicates which proofs will not be asked during the exam.

The new exercises will be posted here on Wednesdays. We expect you to look at the problems over the weekend and to prepare questions for the exercise class on Monday.

Please hand in your solutions by the following Wednesday at 13:00 in your assistant's box in HG J68. Your solutions will usually be corrected and returned in the following exercise class or, if not collected, returned to the box in HG J68.

exercise sheet | due by | solutions | notes |
---|---|---|---|

Exercise sheet 1 | February 28 | Solutions 1 | |

Exercise sheet 2 | March 7 | Solutions 2 | |

Exercise sheet 3 | March 14 | Solutions 3 | |

Exercise sheet 4 | March 21 | Solutions 4 | |

Exercise sheet 5 | March 28 | Solutions 5 | |

Exercise sheet 6 | April 11 | Solutions 6 | Question 2: changed a \(\mathcal{F}\) with \(\overline{\mathcal{F}}\), \(Y\) needs only to be complete. |

Exercise sheet 7 | April 18 | Solutions 7 | |

Exercise sheet 8 | April 25 | Solutions 8 | |

Exercise sheet 9 | May 2 | Solutions 9 | Question 2.b: \(Y = X/K\) and not \(Y= K/A\). |

Exercise sheet 10 | May 9 | Solutions 10 | Note: modified version of Question 2. |

Exercise sheet 11 | May 16 | Solutions 11 | Question 5: Changed \(p^{-1}(z)\) with \(q^{-1}(z)\). |

Exercise sheet 12 | May 23 | Solutions 12 | Question 2 a), need \(X\) and \(Y\) to be path connected. |

Exercise sheet 13 | May 30 | Solutions 13 |

Note: there is no exercise class on Monday the 19th of February.

Please sign in to exercise classes on the echo webpage

time | room | assistant | language |
---|---|---|---|

Mo 10-12 | CHN C 14 | Paul Friedrich | en |

Mo 10-12 | CHN D 48 | Nadir Bayo | en |

Mo 10-12 | ETZ F 91 | Alessio Pellegrini | en |

Mo 10-12 | ETZ H 91 | Alessio Savini | en |

Mo 10-12 | ETZ J 91 | Valentin Bosshard | en |

Mo 10-12 | HG E 33.1 | Tommaso Goldhirsch | en |

The exam will consist of an oral examination of 20 minutes. The list of statemets covered in the lecture can be found here.

"Topology" by James Munkres (Pearson Modern Classics for Advanced Mathematics Series)

"Counterexamples in Topology" by Lynn Arthur Steen, J. Arthur Seebach Jr. (Springer)