General Topology: An Introduction

Main subject categories: • Topology • Topological spaces and generalizations • Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) • Lower separation axioms (T₀–T₃, etc.) • Higher separation axioms • Uniform structures and generalizations • Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces

The first half of the book provides an introduction to general topology, with ample space given to exercises and carefully selected applications.

The second half of the text includes topics in asymmetric topology, a field motivated by applications in computer science. Recurring themes include the interactions of topology with order theory and mathematics designed to model loss-of-resolution situations.

- Applications of metrics include error-correcting codes and social choice.

- Pseudometrics, quasi-metrics, and partial metrics are explored.

- Connections between topology and order are examined.

- Over 740 exercises, from standard to novel, are included.