ABSTRACT
Topology is about geometric properties that are invariant under continuous transformations. An early topological result is the formula of Descartes-Euler relating the number of vertices, edges, and faces of a convex polyhedron. (We will not discuss this here as it is surprisingly difficult to present things rigorously.) After Riemann’s work on surfaces defined by algebraic functions, topology became a key feature in geometry and analysis and nowadays topological ideas are to be found everywhere in mathematics, including number theory. Here we will restrict ourselves to explaining the basic idea of continuity.
