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Homotopy Extension Lemma
Definition: Let X be a space such that X x I is normal. Let A be a closed subspace of X, and let f: A -> Y be a continuous map, where Y is an open subspace of R^n. If f is nulhomotopic, then f may be extended to a continuous map g: X -> Y that is also nulhomotopic.
Source: Topology (second edition) by James R. Munkres