# Topology Spring 2018

Lecturer
Alessandro Sisto
Coordinator
Davide Spriano

## Goal of the course

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.

## Lecture Summaries

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 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.

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.

### Note:

It is possible to hand in exercises in teams of at most three people. The teams are self-organized and may vary from one exercise sheet to the other.

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
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