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