Examples and Counterexamples
- Any Euclidean space is contractible, as is any star domain on a Euclidean space.
- The Whitehead manifold is contractible.
- Spheres of any finite dimension are not contractible.
- The unit sphere in an infinite-dimensional Hilbert space is contractible.
- The house with two rooms is standard example of a space which is contractible, but not intuitively so.
- Dunce hat
- The cone on a Hawaiian earring is contractible (since it is a cone), but not locally contractible or even locally simply connected.
- All manifolds and CW complexes are locally contractible, but in general not contractible.
Read more about this topic: Contractible Space
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“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)