General Topology Chapters 510 [Paperback]

This is the softcover reprint of the 1974 English translation of the later chapters of Bourbakis Topologie Generale. Initial chapters study subgroups and quotients of R, real vector spaces and projective spaces, and additive groups Rn. Analogous properties are then studied for complex numbers. Later chapters illustrate the use of real numbers in general topology and discuss various topologies of function spaces and approximation of functions.

V: One-parameter groups.- ? 1. Subgroups and quotient groups of R.- 1. Closed subgroups of R.- 2. Quotient groups of R.- 3. Continuous homomorphisms of R into itself.- 4. Local definition of a continuous homomorphism of R into a topological group.- ? 2. Measurement of magnitudes.- ? 3. Topological characterization of the groups R and T.- ? 4. Exponentials and logarithms.- 1. Definition of ax and logax.- 2. Behaviour of the functions ax and logax.- 3. Multipliable families of numbers > 0.- Exercises for ? 1.- Exercises for ? 2.- Exercises for ? 3.- Exercises for ? 4.- Historical Note.- VI. Real number spaces and projective spaces.- ? 1. Real number space Rn.- 1. The topology of Rn.- 2. The additive group Rn.- 3. The vector space Rn.- 4. Affine linear varieties in Rn.- 5. Topology of vector spaces and algebras over the field R.- 6. Topology of matrix spaces over R.- ? 2. Euclidean distance, balls and spheres.- 1. Euclidean distance in Rn.- 2. Displacements.- 3. Euclidean balls and spheres.- 4. Stereographic projection.- ? 3. Real projective spaces.- 1. Topology of real projective spaces.- 2. Projective linear varieties.- 3. Embedding real number space in projective space.- 4. Application to the extension of real-valued functions.- 5. Spaces of projective linear varieties.- 6. Grassmannians.- Exercises for ? 1.- Exercises for ? 2.- Exercises for ? 3.- Historical Note.- VII. The additive groupsRn.- ? 1. Subgroups and quotient groups of Rn.- 1. Discrete subgroups of Rn.- 2. Closed subgroups of Rn.- 3. Associatel“)