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## Topology

2019-2020

### Course Objective

At the end of this course:
-the student is familiar with the basic concepts, such as topology, open
and closed sets, and continuous functions, and is able to use these to
prove some fundamental results;
-the student knows several ways to define a topology on a set and can
compare different topologies on the same set;
-the student can determine if a given topological space satisfies
certain properties (such as compactness and connectedness);
-the student understands the concept of topological manifold and
fundamental group, and is aware of the importance of these concepts for
more advanced subjects, such as algebraic topology and differential
geometry.

### Course Content

This course is a first introduction to topology, that is, the
mathematical study of the shape of space. The concepts that are
introduced in this course are essential in understanding more advanced
subjects, such as differential topology, functional analysis, and
algebraic topology.

The following topics will be covered during the course:
-general topological spaces;
-topology generated by a basis;
-continuous maps and homeomorphisms;
-connectedness, path-connectedness, local connectedness;
-compactness, local compactness;
-products and quotients;
-topological manifolds;
-separation axioms;
-the fundamental group of a topological space.

### Teaching Methods

Lectures and tutorials (2+2 hours per week)

### Method of Assessment

For this course there are 4 hand-in assignments (total: 20%), a midterm
examination (30%) and a final exam (50%). There will also be a resit
examination: the final grade will then be determined by the grade of the
resit (80%) and the grade of the hand-in assignments (20%).

### Literature

James R. Munkres, Topology (2nd edition)

### Target Audience

Bachelor Mathematics, year 2

### Recommended background knowledge

-The VU-course Basic concepts of mathematics, in order to be able to
write a proof in a clear and structured manner;
-the VU-courses Analysis 1 and 2, for experience with convergence and
continuity, possibly also in the context of metric spaces;
-the VU-course Group theory for the definition of group and
homomorphisms of groups (this only applies to the last two weeks of this
course).

### General Information

Course Code X_400416 6 EC P4+5 300 English Faculty of Science dr. F. Pasquotto dr. F. Pasquotto dr. F. Pasquotto

### Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture
Target audiences

This course is also available as: