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deformation retract of

Let X$ be a space and let A$ and B$ be subspaces of X$ with A \subset B$. Then A$ is called a deformation retract of B$ over X$ provided that the identity mapping i_B: B \to B$ is homotopic in X$ to a retraction r: B \to A$. Further, A$ is called a strong deformation retract of B$ over X$ provided that it is a deformation retract of B$ over X$ and the homotopy keeps the points of A$ fixed throughout the entire deformation of B$ into A$ (see e.g. [Dugundji 1966, Definition 6.3, p. 324]).
next up previous contents index
Next: dendroid Up: Definitions Previous: decomposable
Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih
2001-11-30