Topologies and Uniformities

A substantially revised edition of the UTM volume, with a view to making the book far more accessible to undergraduates. It contains a larger number of detailed explanations and exercises, together with fully worked solutions to the essential problems and a new chapter on the historical aspects.

Inhalt

1 Topological Spaces.- 2 Continuity.- 3 The Induced Topology and Its Dual.- 4 Open Functions and Closed Functions.- 5 Compact Spaces.- 6 Separation Conditions.- 7 Uniform Spaces.- 8 The Uniform Topology.- 9 Connectedness.- 10 Countability and Related Topics.- 11 Functional Separation Conditions.- 12 Completeness and Completion.- Select Bibliography.- Solutions to Exercises.