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In topology, a retraction is a continuous mapping from a topological space into a subspace that preserves the position of all points in that subspace. The subspace is then called a retract of the original space. A deformation retraction is a mapping that captures the idea of continuously shrinking a space into a subspace.
Definitions, Absolute neighborhood retract (ANR) & No-retraction theorem
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space anr homotopy textstyle retract retraction deformation topological subspace every contractible map locally subset spaces metrizable cw complex neighborhood closed
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