The fundamental concepts of continuity, convergence, and continuous transformation can only be explained and become transparent within the conceptual and construction framework of topology. As such, it is difficult to identify an area of mathematics in which the concepts and language of general topology are not utilized. Topology has a unifying role in mathematics, and a whole series of principles and theorems of general mathematical importance find their natural (i.e. corresponding to the nature of these principles or theorems) formulation only within the framework of general topology. This book emphasizes that topology is a living subject that seeks to understand patterns that permeate the world around us. Although the language of mathematics is based on rules that must be learned, the authors stress the importance for readers move beyond rules and utilize the foundations and fundamentals of general topology. This transformation involves renewed effort to focus on: seeking solutions, not just memorizing procedures; exploring patterns, not just memorizing formulas; and formulating conjectures, not just doing exercises. This approach allows readers to study general topology as an exploratory, dynamic, evolving discipline rather than as a rigid, absolute, closed body of laws to be memorized. Chapter coverage includes: Topological Spaces and Continuous Functions; Topology of the Line and Plane; Induced and Coinduced Topologies; Topological Vector Spaces; Continuity and Topological Equivalence; Connectedness, Compactness, and Continuity; Convergence Separation and Countability Axioms; Metric, Function, Uniform, and Compact Spaces; Mapping of Spaces and Product and Quotient Spaces; Baire Spaces and Dimension Theory; Classification of Covering Spaces; and Embedding and Metrication.
