Homotopy type is a concept in algebraic topology that captures the essential topological features of a space by classifying spaces based on their homotopy equivalence. Two spaces are said to have the same homotopy type if there exists a continuous deformation, or homotopy, between them that preserves their fundamental structure. This idea is closely tied to the notion of relative homology groups, where one studies the properties of a space relative to a subspace, highlighting how the structure of the space can change while preserving its essential characteristics.
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