Category:Homotopy Equivalences
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This category contains results about Homotopy Equivalences.
Definitions specific to this category can be found in Definitions/Homotopy Equivalences.
Let $X$ and $Y$ be topological spaces.
Let $f: X \to Y$ be a continuous mapping.
Let there exist a continuous mapping $g: Y \to X$ such that:
- the composite mapping $g \circ f$ is homotopic to the identity mapping $I_X$ on $X$
- the composite mapping $f \circ g$ is homotopic to the identity mapping $I_Y$ on $Y$.
Then $X$ and $Y$ are homotopy equivalent.
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