Weakly contractible

In mathematics, a topological space is said to be weakly contractible if all of its homotopy groups are trivial.

Property

It follows from Whitehead's Theorem that if a CW-complex is weakly contractible then it is contractible.

Example

Define to be the inductive limit of the spheres . Then this space is weakly contractible. Since is moreover a CW-complex, it is also contractible. See Contractibility of unit sphere in Hilbert space for more.

gollark: Outside of timestamps, which are small and thus insignificant, no.
gollark: ESPECIALLY given that I plan to store stuff like edit distance.
gollark: But that would be somewhat inelegant.
gollark: > This isn't really ideal, as I think I'm duplicating data a bit (timestamps), updating a page involves more work, and more importantly the revisions thing doesn't have any relevant information beyond what's available from pages.> Also, the latest update to something doesn't show on the user-visible revisions page, which is a minor nitpick but I mildly dislike it.
gollark: Hold on while I checkinate.

References

  • "Homotopy type", Encyclopedia of Mathematics, EMS Press, 2001 [1994]


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