# Weakly contractible

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