Lecture Notes on Point-Set Topology

Author: Xiong Jincheng
Publisher:
Publish Date: 2003-12-01
Features: This book covers the fundamental knowledge of point-set topology, with its basic content including: the definitions and basic properties of topological spaces and continuous mappings; methods for constructing new topological spaces; various topological invariants such as connectedness, separation, compactness, and the completeness of metric spaces, as well as the relationships among these topological invariants; integrable and hereditary properties of these topological invariants; mapping spaces and their various basic topologies. This revised edition specifically includes a chapter on fundamental groups and their applications, while also supplementing and refining the content on naive set theory, introducing some commonly used propositions equivalent to the axiom of choice. This book can serve as a textbook or reference for point-set topology courses in mathematics-related disciplines. It includes the definitions and basic properties of topological spaces and continuous mappings, methods for constructing new topological spaces, various topological invariants and their interrelationships, as well as mapping spaces and their various basic topologies.