Topology, 3 hours lecture, WS 2014/15, Mon, Tue early afternoon, lecturer G. Propst, KFU

Topology is the theory of topological spaces, i.e. structures between which continuous maps are definable.

In generalization of the geometry with rigid transformations, two geometric objects are topologically equivalent, if there exist bijective continuous maps between them.

A large class of topological spaces are the metric spaces in analysis. However, there is a need of non metrizable spaces (eg. the space of test functions for distributions or the weak topologies in functional analysis). This is the theme of set-theoretic topology.

In order to classify them, algebraic topology associates groups to topological spaces.

Thus, abstract topological concepts play a fundamental role in various fields of mathematics. These concepts will be introduced and explained, with an emphasis on set-theoretic topology (convergence, compactness, connectedness, separation properties).

On request the lecture will be held in English. Parts of "A Taste of Topology" by V. Runde will serve as reference.

Supplements (not to be examined):

• Elementare geometrische Topologie (Arnold)

• Lokal konvexe Raeume (Werner)

• Kategorien (Laures/Szymik)

• Filter (Laures/Szymik)

• Algebraic Topology (Runde)