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A space homotopy equivalent to a point.
Contractibility is an existence property. A chosen contraction would be additional pointed homotopy data, not part of the ordinary notion.
wp-contractiblenlab-contractiblehatcher-algebraic-topologyEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require the identity map to be homotopic to a constant map. A particular contraction is not part of the structure.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-contractiblenlab-contractiblehatcher-algebraic-topologyEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Every nonempty contractible space is path-connected.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-contractiblenlab-contractiblewp-path-connectednlab-path-connectedhatcher-algebraic-topology