V: One-parameter groups.- § 1. Subgroups and quotient groups of R.- § 2. Measurement of magnitudes.- § 3. Topological characterization of the groups R and T.- § 4. Exponentials and logarithms.- 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.- § 2. Euclidean distance, balls and spheres.- § 3. Real projective spaces.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Historical Note.- VII. The additive groupsRn.- § 1. Subgroups and quotient groups of Rn.- § 2. Continuous homomorphisms of Rn and its quotient groups.- § 3. Infinite sums in the groups Rn.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Historical Note.- VIII. Complex numbers.- § 1. Complex numbers, quaternions.- § 2. Angular measure, trigonometric functions.- § 3. Infinite sums and products of complex numbers.- § 4. Complex number spaces and projective spaces.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Exercises for § 4.- Historical Note.- IX. Use of real numbers in general topology.- § 1. Generation of a uniformity by a family of pseudometrics; uniformizable spaces.- § 2. Metric spaces and metrizable spaces.- § 3. Metrizable groups, valued fields, normed spaces and algebras.- § 4. Normal spaces.- § 5. Baire spaces.- § 6. Polish spaces, Souslin spaces, Borel sets.- Appendix: Infinite products in normed algebras.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Exercises for § 4.- Exercises for § 5.- Exercises for § 6.- Exercises for the Appendix.- Historical Note.- X. Function spaces.- §1. The uniformity of 𝔖-convergence.- § 2. Equicontinuous sets.- § 3. Special function spaces.- § 4. Approximation of continuous real-valued functions.- Exercises for § 1.- Exercises for § 2.- Exercises for § 3.- Exercises for § 4.- Historical Note.- Index of Notation.- Index of Terminology.
