Hjem

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 -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.