**Locally Contractible Spaces**

A topological space is **locally contractible** if every point has a local base of contractible neighborhoods. Contractible spaces are not necessarily locally contractible nor vice-versa. For example, the comb space is contractible but not locally contractible (if it were, it would be locally connected which it is not). Locally contractible spaces are locally *n*-connected for all *n* ≥ 0. In particular, they are locally simply connected, locally path connected, and locally connected.

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### Famous quotes containing the words spaces and/or locally:

“Le silence éternel de ces espaces infinis m’effraie. The eternal silence of these infinite *spaces* frightens me.”

—Blaise Pascal (1623–1662)

“To see ourselves as others see us can be eye-opening. To see others as sharing a nature with ourselves is the merest decency. But it is from the far more difficult achievement of seeing ourselves amongst others, as a local example of the forms human life has *locally* taken, a case among cases, a world among worlds, that the largeness of mind, without which objectivity is self- congratulation and tolerance a sham, comes.”

—Clifford Geertz (b. 1926)