homotopy
Americannoun
-
homotopies
plural
Other Word Forms
Noun Inflected Forms
Etymology
Origin of homotopy
1915–20; homo- + -topy (< Greek tóp ( os ) place + -y 3, or < New Latin -topia )
Example Sentences
Examples are provided to illustrate real-world usage of words in context. Any opinions expressed do not reflect the views of Dictionary.com.
See Examples For:
The researchers provide a unified skyrmion-hopfion homotopy classification and offer an insight into the diversity of topological solitons in three-dimensional chiral magnets.
From Science Daily ● Nov. 22, 2023
A homotopy equivalence is another type of continuous deformation, but in this case, you can identify distinct points.
From Scientific American ● Sep. 14, 2021
These proof assistants have a mechanism that mimics the common mathematical practice of transferring information about one thing to another thing that is understood to be the same via an explicit isomorphism or homotopy equivalence.
From Scientific American ● Sep. 14, 2021
Motivic homotopy theory is blossoming, despite Voevodsky’s change of focus about ten years ago.
From Nature
In Voevodsky’s motivic homotopy theory, familiar classical geometry was replaced by homotopy theory — a branch of topology in which a line may shrink all the way down to a point.
From Nature
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.
From Scientific American ● Sep. 14, 2021
For example, in π ∞ X the objects and arrows are the points and the paths—no longer considered up to wiggling—while the higher-dimensional transformations encode the higher homotopies.
From Scientific American ● Sep. 14, 2021
These deformations, which are technically called homotopies, are necessary for the composition of paths to define an associative operation, as is required by a category.
From Scientific American ● Sep. 14, 2021
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