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In topology, a branch of mathematics, two continuous functions from one topological space to another are called **homotopic** (from Ancient Greek: ὁμός *homós* "same, similar" and τόπος *tópos* "place") if one can be "continuously deformed" into the other, such a deformation being called a **homotopy** (/həˈmɒtəpiː/,^{[1]} *hə-MO-tə-pee*; /ˈhoʊmoʊˌtoʊpiː/,^{[2]} *HOH-moh-toh-pee*) between the two functions. A notable use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology.^{[3]}

In practice, there are technical difficulties in using homotopies with certain spaces. Algebraic topologists work with compactly generated spaces, CW complexes, or spectra.

**^**"Homotopy Definition & Meaning". Retrieved 22 April 2022.`{{cite web}}`

: CS1 maint: url-status (link)**^**"Homotopy Type Theory Discussed - Computerphile".*YouTube*. Retrieved 22 April 2022.`{{cite web}}`

: CS1 maint: url-status (link)**^**"Homotopy | mathematics".*Encyclopedia Britannica*. Retrieved 2019-08-17.