homotopy

[huh-mot-uh-pee, hoh-]

noun

Mathematics.

plural

homotopies 

1. the relation that exists between two mappings in a topological space if one mapping can be deformed in a continuous way to make it coincide with the other.

Word History and Origins

Origin of homotopy¹

1915–20; homo- + -topy (< Greek tóp ( os ) place + -y ³, or < New Latin -topia )

Example Sentences

The researchers provide a unified skyrmion-hopfion homotopy classification and offer an insight into the diversity of topological solitons in three-dimensional chiral magnets.

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Sullivan says that the result he is proudest of is one he obtained in 1977, which distils the crucial properties of a space using a tool called rational homotopy.

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But contractability guarantees that any two composite paths are homotopic, any two homotopies relating two composite paths are connected by a higher homotopy, and so on.

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This term refers to the notion of isomorphism in the more exotic homotopy category of spaces.

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A homotopy equivalence is another type of continuous deformation, but in this case, you can identify distinct points.

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