Elements of mathematics /

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 gnrale. It gives all the basics of the subject, starting from definitions. Important classes of topological spaces are studied, uniform structure...

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Bibliographic Details
Main Author:	Bourbaki, Nicolas
Corporate Author:	SpringerLink (Online service)
Format:	eBook
Language:	English
Published:	Berlin : Springer, 1998.
Subjects:	Topology. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

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
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
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 IIV)
Index of Terminology (Chapters IIV).