Topological Spaces

Topological Spaces: From Distance to Neighborhood is a gentle introduction to topological spaces leading the reader to understand the notion of what is important in topology vis-a-vis geometry. The authors have carefully divided the book into three sections; The line and the plane, Metric spaces and Topological spaces, in order to mitigate the the move into higher levels of abstraction. Students will be very attracted to this presentation.

Résumé
Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.

Contenu
I The Line And The Plane.- 1 What Topology Is About.- 2 Axioms for ?.- 3 Convergent Sequences and Continuity.- 4 Curves in the Plane.- II Metric Spaces.- 5 Metrics.- 6 Open and Closed Sets.- 7 Completeness.- 8 Uniform Convergence.- 9 Sequential Compactness.- 10 Convergent Nets.- 11 Transition to Topology.- III Topological Spaces.- 12 Topological Spaces.- 13 Compactness and the Hausdorff Property.- 14 Products and Quotients.- 15 The Hahn-Tietze-Tong-Urysohn Theorems.- 16 Connectedness.- IV Postscript.- 18 A Smorgasbord for Further Study.- 19 Countable Sets.- Literature.- Index of Symbols.- Index of Terms.