MATH3281
Lecturer : Dirk Schuetz
Term : Michaelmas 2012
Lectures :Problems classes:
Literature
The following is a list of books on which the lecture is based. Although we will not follow a book strictly, the material can be found in them and they may sometimes offer a different approach.Assignments
Homework | Date | Hand in | Solutions |
Problem Set 1 pdf | 16.10.12 | - | |
Problem Set 2 pdf | 29.10.12 | 06.11.12 | |
Problem Set 3 pdf | 12.11.12 | - | |
Problem Set 4 pdf | 26.11.12 | 04.12.12 | |
Problem Set 5 pdf | 10.12.12 | - |
Lecture Outline
Date | Outline |
11.12. | In this lecture we define real projective space and lens spaces, and show that SO(n) is connected. |
10.12. | In this lecture we discuss the action of the 3-sphere on 3-dimensional Euclidean space, orbits and orbit spaces. |
04.12. | In this lecture we show that O(n) is compact, define operations of topological groups on topological spaces, and discuss several such examples. |
03.12. | In this lecture we define topological groups and give plenty of examples. In particular, we show that the 3-sphere is a topological group. |
27.11. | In this lecture we have a closer look at the quotient topology, define identification maps and construct the Möbius band and the Klein bottle. |
26.11. | In this lecture we look at the Bolzano-Weierstrass Theorem and the Lebesgue Lemma, before defining quotient spaces and discussing some of their properties. |
20.11. | In this lecture we prove the Heine-Borel Theorem, thus giving a convenient criterion for compact subspaces in Euclidean space. We also discuss useful applications of it. |
19.11. | In this lecture we show that [0,1] is compact, and discuss all sorts of nice properties of compact spaces. |
13.11. | In this lecture we explain the difference between path-connectedness and connectedness, and introduce the concept of compactness. |
12.11. | In this lecture we look at more properties of connectedness, see more examples and compare it to path-connectedness. |
06.11. | In this lecture we give more examples of connected spaces, and look at some of their properties involving continuity. |
05.11. | In this lecture we have a closer look at some properties of the product topology, and consider the concept of connectedness. |
30.10. | In this lecture we define a basis of a topology, give equivalent notions of continuity using bases, closures etc, and look at product spaces. |
29.10. | In this lecture we deal with limit points, define the interior and the closure of a set, and see various examples. |
23.10. | In this lecture we define Hausdorff spaces, see that not every topological space is metric, and deal with continuity. |
22.10. | In this lecture we see examples of topological spaces, show how metric spaces fit into this concept, and look at closed sets. |
16.10. | In this lecture we relate open sets to continuity in metric spaces, and define topological spaces. |
15.10. | In this lecture we will define open and closed sets in metric spaces, and discuss some of their properties. |
09.10. | In this lecture we will look at convergence in metric spaces, define continous functions, and look at relations between them. |
08.10. | In this lecture we will define metric spaces, and give various examples of them. |