General Topology Chapters 14 [Paperback]

This is the softcover reprint of the 1971 English translation of the first four chapters of Bourbakis Topologie Generale. It gives all basics of the subject, starting from definitions. Important classes of topological spaces are studied, and uniform structures are introduced and applied to topological groups. In addition, real numbers are constructed and their properties established.

This is the softcover reprint of the English translation of 1971 (available from Springer since 1989) of the first 4 chapters of Bourbaki's Topologie g?n?rale. It gives all the basics of the subject, starting from definitions. Important classes of topological spaces are studied, uniform structures are introduced and applied to topological groups. Real numbers are constructed and their properties established. Part II, comprising the later chapters, Ch. 5-10, is also available in English in softcover.of the Elements of Mathematics Series.- I. Topological Structures.- ? 1. Open sets, neighbourhoods, closed sets.- 1. Open sets.- 2. Neighbourhoods.- 3. Fundamental systems of neighbourhoods; bases of a topology.- 4. Closed sets.- 5. Locally finite families.- 6. Interior, closure, frontier of a set; dense sets.- ? 2. Continuous functions.- 1. Continuous functions.- 2. Comparison of topologies.- 3. Initial topologies.- 4. Final topologies.- 5. Pasting together of topological spaces.- ? 3. Subspaces, quotient spaces.- 1. Subspaces of a topological space.- 2. Continuity with respect to a subspace.- 3. Locally closed subspaces.- 4. Quotient spaces.- 5. Canonical decomposition of a continuous mapping.- 6. Quotient space of a subspace.- ? 4. Product of topological spaces.- 1. Product spaces.- 2. Section of an open set; section of a closed set, projection of an open set. Partial continuity.- 3. Closure in a product.- 4. Inverse limits of topological spaces.- ? 5. Open mappings and closed mappings.- 1. Open mappings and closed mappings.- 2. Open equivalence relal+