EN
Contents
Introduction............................................................................................................................................................................... 3
§ 1. Historical development of the concept of a geometric object..................................................................................4
§ 2. Manifold, coordinate system, transformations of the coordinate system............................................................. 7
§ 3. Group, pseudogroup, groupoid.................................................................................................................................... 9
§ 4. Wundheiler's definition of a geometric object........................................................................................................... 15
§ 5. Special geometric objects............................................................................................................................................. 18
§ 6. Abstract geometric object. The Haantjes-Laman definition of a geometric object............................................. 24
§ 7. Classification of geometric objects.............................................................................................................................. 28
§ 8. Equivalence of geometric objects................................................................................................................................ 39
§ 9. Fibres of equivalent geometric objects....................................................................................................................... 42
§ 10. Concomitants................................................................................................................................................................. 47
§ 11. Algebra of geometric objects...................................................................................................................................... 54
§ 12. Differential concomitants............................................................................................................................................. 57
References............................................................................................................................................................................... 63