OverviewThis module is an introduction to point-set topology, a topic that is relevant to many other areas of mathematics. In it, we will be looking at the concept of topological spaces and related constructions. In an Euclidean space, an "open set" is defined as a (possibly infinite) union of open "epsilon-balls". A topological space generalises the notion of "open set" axiomatically, leading to some interesting and sometimes surprising geometric consequences. For example, we will encounter spaces where every sequence of points converges to every point in the space, see why for topologists a doughnut is the same as a coffee cup, and have a look at famous objects such as the Moebius strip or the Klein bottle.
This module appears in:
Method of assessment
80% Examination, 20% Coursework
J.G. Hocking and G. Young: Topology, Dover Publications, 1988
J.R. Munkres: Topology, a first course, Prentice-Hall, 1975
C. Adams and A. Franzosa: Introduction to Topology, pure and applied, Pearson Prentice-Hall, 2008
The intended subject specific learning outcomes. On successful completion of this module, students will be able to:
1 understand the basic concepts of topology;
2 apply notions from point-set topology to problems in geometry;
3 appreciate non-Euclidean geometric concepts;
4 develop awareness of relations to other mathematical areas such as Calculus, Metric Spaces
and Functional Analysis.
The intended generic learning outcomes. On successful completion of the module, the students will have:
1 an enhanced ability to reason and deduce confidently from given definitions and constructions;
2 enhanced knowledge of associated abstract geometric concepts with applications;
3 matured in their problem formulating and solving skills;
4 consolidated their grasp of a wide variety of mathematical skills and methods.