General Topology Chapters 1–4
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 générale. It gives all the basics of the subject, starting from definitions. Important classes of topological spaces are studied, uniform structu...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1995, 1995
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| Edition: | 1st ed. 1995 |
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- § 8. Usual expansions of real numbers; the power of R
- Exercises for § 1
- Exercises for § 2
- Exercises for § 3
- Exercises for § 4
- Exercises for § 5
- Exercises for § 6
- Exercises for § 7
- Exercises for § 8
- Historical Note
- Index of Notation (Chapters I–IV)
- Index of Terminology (Chapters I–IV)
- III: Topological Groups
- § 1. Topologies on groups
- § 2. Subgroups, quotient groups, homomorphisms, homogeneous spaces, product groups
- § 3. Uniform structures on groups
- § 4. Groups operating properly on a topological space; compactness in topological groups and spaces with operators
- § 5. Infinite sums in commutative groups
- § 6. Topological groups with operators; topological rings, division rings and fields
- § 7. Inverse limits of topological groups and rings
- Exercises for § 1
- Exercises for § 2
- Exercises for § 3
- Exercises for § 4
- Exercises for § 5
- Exercises for § 6
- Exercises for § 7
- Historical Note
- IV: Real Numbers
- § 1. Definition of real numbers
- § 2. Fundamental topological properties of the real line
- § 3. The field of real numbers
- § 4. The extended real line
- § 5. Real-valued functions
- § 6. Continuous and semi-continuous real-valued functions
- § 7. Infinite sums and products of real numbers
- of the Elements of Mathematics Series
- I. Topological Structures
- § 1. Open sets, neighbourhoods, closed sets
- § 2. Continuous functions
- § 3. Subspaces, quotient spaces
- § 4. Product of topological spaces
- § 5. Open mappings and closed mappings
- § 6. Filters
- § 7. Limits
- § 8. Hausdorff spaces and regular spaces
- § 9. Compact spaces and locally compact spaces
- § 10. Proper mappings
- §11. Connectedness
- Exercises for § 1
- Exercises for § 2
- Exercises for § 3
- Exercises for § 4
- Exercises for § 5
- Exercises for § 6
- Exercises for § 7
- Exercises for § 8
- Exercises for § 9
- Exercises for § 10
- Exercises for § 11
- Historical Note
- II. Uniform Structures
- § 1. Uniform spaces
- § 2. Uniformly continuous functions
- § 3. Complete spaces
- § 4. Relations between uniform spaces and compact spaces
- Exercises for § 1
- Exercises for § 2
- Exercises for § 3
- Exercises for § 4
- Historical Note