- 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.

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 | |

Exercise sheet on covering | Solutions covering |

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)