Book:Ryszard Engelking/General Topology/Revised and Completed Edition

Subject Matter

 * Topology

Contents

 * Preface to the first edition
 * Preface to the revised edition


 * Introduction
 * I.1 Algebra of sets. Functions
 * I.2 Cardinal numbers
 * I.3 Order relations. Ordinal numbers
 * I.4 The axiom of choice
 * I.5 Real numbers


 * Chapter 1: Topological spaces
 * 1.1 Topological spaces. Open and closed sets. Bases. Closure and interior of a set
 * 1.2 Methods of generating topologies
 * 1.3 Boundary of a set and derived set. Dense and nowhere dense sets. Borel sets
 * 1.4 Continuous mappings. Closed and open mappings. Homeomorphisms
 * 1.5 Axioms of separation
 * 1.6 Convergence in topological spaces: Nets and filters. Sequential and Fréchet spaces
 * 1.7 Problems


 * Chapter 2: Operations on topological spaces
 * 2.1 Subspaces
 * 2.2 Sums
 * 2.3 Cartesian products
 * 2.4 Quotient spaces and quotient mappings
 * 2.5 Limits of inverse systems
 * 2.6 Function spaces I: The topology of uniform convergence on RX and the topology of pointwise convergence
 * 2.7 Problems


 * Chapter 3: Compact spaces
 * 3.1 Compact spaces
 * 3.2 Operations on compact spaces
 * 3.3 Locally compact spaces and $k$-spaces
 * 3.4 Function spaces II: The compact-open topology
 * 3.5 Compactifications
 * 3.6 The Cech-Stone compactification and the Wallman extension
 * 3.7 Perfect mappings
 * 3.8 Lindelöf spaces
 * 3.9 Cech-complete spaces
 * 3.10 Countably compact spaces, pseudocompact spaces and sequentially compact spaces
 * 3.11 Realcompact spaces
 * 3.12 Problems


 * Chapter 4: Metric and metrizable spaces
 * 4.1 Metric and metrizable spaces
 * 4.2 Operations on metrizable spaces
 * 4.3 Totally bounded and complete metric spaces. Compactness in metric spaces
 * 4.4 Metrization theorems I
 * 4.5 Problems


 * Chapter 5: Paracompact spaces
 * 5.1 Paracompact spaces
 * 5.2 Countably paracompact spaces
 * 5.3 Weakly and strongly paracompact spaces
 * 5.4 Metrization theorems II
 * 5.5 Problems


 * Chapter 6: Connected spaces
 * 6.1 Connected spaces
 * 6.2 Various kinds of disconnectedness
 * 6.3 Problems


 * Chapter 7: Dimension of topological spaces
 * 7.1 Definitions and basic properties of dimensions ind, Ind, and dim
 * 7.2 Further properties of the dimension dim
 * 7.3 Dimension of metrizable spaces
 * 7.4 Problems


 * Chapter 8: Uniform spaces and proximity spaces
 * 8.1 Uniformities and uniform spaces
 * 8.2 Operations on uniform spaces
 * 8.3 Totally bounded and complete uniform spaces. Compactness in uniform spaces
 * 8.4 Proximities and proximity spaces
 * 8.5 Problems


 * Bibliography


 * Tables
 * Relations between main classes of topological spaces
 * Invariants of operations
 * Invariants and inverse invariants of mappings


 * List of special symbols
 * Author index
 * Subject index