homotopy
noun
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.
homotopies
-
pluralof homotopy.plural
The grammatical form denoting more than one person, place, thing, or idea.
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.
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
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
