Topologie II (voorjaar 2005)

• Classical dimension theory.
Description: Dimension theory enables us to assign to every topological space X an integer, dim X, having, among other things, the following properties: (1) if X and Y are homeomorphic spaces then dim X = dim Y, (2) dim R^n = n for every n. So dim X, the topological dimension of X, is a topological invariant of X, and by (2) it distinguishes between the euclidean spaces R^n. The aim of this course is to present some basic results from dimension theory. Some of the presented results are classical. During the last decades significant contributions were made concerning the topology of so-called infinite-dimensional spaces and the topology of hereditarily indecomposable continua. We shall also present some of these results in detail.
Prerequisites: Topology I.
Examination: Oral.
Literature: For the lecture notes, click here (we will basically cover Chapter 3 (and more) in The infinite-dimensional topology of function spaces).