1st semester 
20 credits / 30 lectures

The secret of success in pure mathematics is not to attempt the greatest level of generality, but the right one for the context and problems you want to solve. General topology is extensively used for many reasons, including: (1) the axioms defining a topological space are extremely simple, (2) this leads to a plethora of examples, and (3) a topological space is exactly the right setting in which to discuss questions of convergence and continuity, which you will already be familiar with from real analysis and metric spaces. My aim is to introduce you to a whole new world, in which you will learn famous theorems created by those who came before you, but will also become adept at producing examples and results yourself. This is certainly a demanding module, for those who value pure mathematics for its own sake. That said, it will provide many classical results and tools used by people working in other areas of mathematics.