homotopy extension property


Let X be a topological spaceMathworldPlanetmath and A a subspaceMathworldPlanetmath of X. Suppose there is a continuous mapMathworldPlanetmath f:X→Y and a homotopy of maps F:A×I→Y. The inclusion map i:A→X is said to have the homotopy extension property if there exists a continuous map F′ such that the following diagram commutes:

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