Table of contents

CONTENTS Introduction § 1. Definition of cohomological dimension § 2. Bokshtein's inequalities § 3. Cohomological manifolds over finite groups § 4. The CE-problem § 5. Borsuk's problem References

CONTENTS Introduction § 1. Euler's method. The basic statements § 2. Non-standard analysis § 3. The derivation of Euler's factorizations using non-standard analysis § 4. Euler's construction in the system of non-standard analysis § 5. Factors and coefficients in Euler's construction § 6. A factorization that Euler did not want to complete § 7. The summation of infinitesimals § 8. Formal infinity as a mathematical object § 9. Representations of the exponential as a series and as a power § 10. Comparing the coefficients of non-standard polynomials Conclusion References

CONTENTS Introduction § 1. Absolute and relative results § 2. Change in research plans § 3. Metamathematics in general topology § 4. Major new lines of investigation Conclusion References

CONTENTS Introduction Part I. Definition and basic properties of dimension and capacity characteristics § 1. Construction of dimension and capacity characteristics § 2. Properties of dimension and capacity characteristics Part II. Examples of dimension and capacity characteristics § 3. Classical dimension and capacity characteristics § 4. Topological pressure and topological entropy § 5. Metric entropy characteristics § 6. Dimension and capacity characteristics relative to a mapping Appendix A. A variational principle for non-compact sets Appendix B. Dynamical invariants of Takens Appendix C. Carathéodory-measurable sets References

CONTENTS § 0. Introduction § 1. Extended version of some Morse constructions § 2. Potential flows § 3. Superposition of a vortex on a simple passage § 4. Superposition of a vortex on a reverse flow § 5. Analytic uniqueness theorem References