Institutionernas doktorandkurser

Basic introduction to topology with a geometric flavour. The concepts of a topological space and continuous functions are introduced and their general properties discussed. In particular compactness, various forms of conectedness and separation axioms are covered as well as quotient spaces. Examples include topological groups and group actions on spaces. The fundamental group of a space is constructed and used to obtain some classical low-dimensional results in geometry. Simplicial spaces are defined and the simplicial approximation theorem proved.