Topology of Surfaces, Knots, and Manifolds

"Since the early part of the 20th century both topology and analysis have fed off each other and this has resulted in some very beautiful theorems that lie at the interface between these two disciplines. Perhaps the best known example of these is Brouwer's fixed point theorem (later generalised by J. Schauder to more general spaces) which has had countless applications in applied mathematics, economics and analysis itself. Topology is the study of those properties of objects that are preserved under careful deformation. Topology is the area of mathematics which investigates continuity and related concepts. Important fundamental notions soon to come are for example open and closed sets, continuity, and homeomorphism. Originally coming from questions in analysis and differential geometry, by now topology permeates mostly every field of math including algebra, combinatorics, logic, and plays a fundamental role in algebraic/arithmetic geometry as we know it today. s Topology of Surfaces, Knots, and Manifolds offers an intuition-based and applied approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds. A comprehensive, self-contained treatment presenting general results of the theory."