The course covers the basic notions in set topology. Set topology is a big and important keystone in modern mathematics. From calculus in several variables, you should be acquainted with the three dimensional space and its distance notions. In topology, we distance ourselves from distance notions and real valued functions. Instead, we start from a collection of subsets to a given set. The elements of the collection are called open. By using these we build a theory for topological spaces and continuous functions. Classical continuity arguments can then be used in new and often unexpected situations. Some important types of topological spaces are for example compact and coherent topological spaces. Those properties can help us to decide if two topological spaces are topologically identical, i.e. if they are homomorphic. This will e.g. induce that a compact space can not be homomorphic with a non-compact space and a coherent space can not be homomorphic with non-coherent space. This course is mainly for students who like mathematical proofs and abstractions. For those who have not taken more than one course in calculus in several variables, an insight into the world of topology can be both refreshing and eye-opening.
