| 11. | Hopf proved that the Hopf map has Hopf invariant 1, and therefore is not null-homotopic.
|
| 12. | Two mappings are "'homotopic "'if one can be continuously deformed into the other.
|
| 13. | At any rate, we can see that there are gauge transformations U homotopic to the trivial gauge transformation.
|
| 14. | The "'Borel conjecture "'states that the map f is homotopic to a homeomorphism.
|
| 15. | A weak form of Tutte's homotopy theorem states that any closed path is homotopic to the trivial path.
|
| 16. | The Hawaiian earring is not simply connected, since the loop parametrising any circle is not homotopic to a trivial loop.
|
| 17. | Under what conditions is f homotopic to the identity \ text { id } _ T : T \ to T.
|
| 18. | With Jack Snoeyink he extended the algorithms for simple polygons to compute homotopic shortest paths among polygonal obstacles in the plane.
|
| 19. | The gluing map is homotopic to the identity map on the circle and so the complex is homotopy equivalent to the disc.
|
| 20. | In this sense, the homotopy pushouts treats homotopic spaces as well as the ( ordinary ) pushout does with homeomorphic spaces.
|
