21. However these two sets have an intersection that forms a non-contractible equatorial band. 22. Every contractible space is simply connected. 23. It is path-connected, locally path-connected and simply connected but not contractible . 24. Affine space is topologically contractible , so it admits no non-trivial topological vector bundles. 25. One can ask whether " all " contractible manifolds are homeomorphic to a ball. 26. A contractible manifold is one that can continuously be shrunk to a point inside the manifold itself. 27. This has yielded noncontractible loops of Legendrian knots which are contractible in the space of all knots. 28. Could anyone please link me to a proof that a compact manifold without boundary is not contractible ? 29. The double cover of this space is the infinite sphere S ^ \ infty, which is contractible . 30. Intuitively, a contractible space is one that can be continuously shrunk to a point within that space.
