General Topology

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.