A topological space is said to be contractible if it is homotopy equivalent to a point. Equivalently, the space is contractible if a constant map is homotopic to the identity map. A contractible space has a trivial fundamental group.
An important property, any vector bundle defined on a contractible open set is trivial.
A contractible space is simply connected.
Star-shaped spaces are contractible.
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Author of the notes: Antonio J. Pan-Collantes
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