General Topology

Abstract

General or set-theoretical topology is the theory of continuity and convergence in analysis. Although the theory draws its notions and fundamental examples from geometry (so that the reader is advised always to think of a topological space as something resembling the euclidean plane), it applies most often to infinite-dimensional spaces of functions, for which geometrical intuition is very hard to obtain. Topology allows us to reason in these situations as if the spaces were the familier two- and three-dimensional objects, but the process takes a little time to get used to.