Author | Bourbaki, Nicolas. author |
---|---|
Title | General Topology [electronic resource] : Chapters 1-4 / by Nicolas Bourbaki |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1995 |
Connect to | http://dx.doi.org/10.1007/978-3-642-61701-0 |
Descript | VII, 437 p. online resource |
of the Elements of Mathematics Series -- I. Topological Structures -- ยง 1. Open sets, neighbourhoods, closed sets -- ยง 2. Continuous functions -- ยง 3. Subspaces, quotient spaces -- ยง 4. Product of topological spaces -- ยง 5. Open mappings and closed mappings -- ยง 6. Filters -- ยง 7. Limits -- ยง 8. Hausdorff spaces and regular spaces -- ยง 9. Compact spaces and locally compact spaces -- ยง 10. Proper mappings -- ยง11. Connectedness -- Exercises for ยง 1 -- Exercises for ยง 2 -- Exercises for ยง 3 -- Exercises for ยง 4 -- Exercises for ยง 5 -- Exercises for ยง 6 -- Exercises for ยง 7 -- Exercises for ยง 8 -- Exercises for ยง 9 -- Exercises for ยง 10 -- Exercises for ยง 11 -- Historical Note -- II. Uniform Structures -- ยง 1. Uniform spaces -- ยง 2. Uniformly continuous functions -- ยง 3. Complete spaces -- ยง 4. Relations between uniform spaces and compact spaces -- Exercises for ยง 1 -- Exercises for ยง 2 -- Exercises for ยง 3 -- Exercises for ยง 4 -- Historical Note -- III: Topological Groups -- ยง 1. Topologies on groups -- ยง 2. Subgroups, quotient groups, homomorphisms, homogeneous spaces, product groups -- ยง 3. Uniform structures on groups -- ยง 4. Groups operating properly on a topological space; compactness in topological groups and spaces with operators -- ยง 5. Infinite sums in commutative groups -- ยง 6. Topological groups with operators; topological rings, division rings and fields -- ยง 7. Inverse limits of topological groups and rings -- Exercises for ยง 1 -- Exercises for ยง 2 -- Exercises for ยง 3 -- Exercises for ยง 4 -- Exercises for ยง 5 -- Exercises for ยง 6 -- Exercises for ยง 7 -- Historical Note -- IV: Real Numbers -- ยง 1. Definition of real numbers -- ยง 2. Fundamental topological properties of the real line -- ยง 3. The field of real numbers -- ยง 4. The extended real line -- ยง 5. Real-valued functions -- ยง 6. Continuous and semi-continuous real-valued functions -- ยง 7. Infinite sums and products of real numbers -- ยง 8. Usual expansions of real numbers; the power of R -- Exercises for ยง 1 -- Exercises for ยง 2 -- Exercises for ยง 3 -- Exercises for ยง 4 -- Exercises for ยง 5 -- Exercises for ยง 6 -- Exercises for ยง 7 -- Exercises for ยง 8 -- Historical Note -- Index of Notation (Chapters I-IV) -- Index of Terminology (Chapters I-IV)