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 $S^{\infty }$ to be the inductive limit of the spheres $S^{n},n\geq 1$ . Then this space is weakly contractible. Since $S^{\infty }$ is moreover a CW-complex, it is also contractible. See Contractibility of unit sphere in Hilbert space for more.

gollark: There's a 69% chance that you will and a 39% chance you won't.

gollark: Only 103% of PotatOS users should be using it.

gollark: 62% of people know how, 86% don't, 20% of people can't use a computer anyway, 10% complain that I don't understand percentages.

gollark: Many don't even know about mounting computers as disks.

gollark: Or `set potatOS.really_boring true` before install.

References

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

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