# homotopy

## homotopy

[huh-mot-uh-pee, hoh-]
noun, plural homotopies. Mathematics.
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.

Origin:
1915–20; homo- + -topy (< Greek tóp(os) place + -y3, or < Neo-Latin -topia)

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homotopy

in mathematics, a way of classifying geometric regions by studying the different types of paths that can be drawn in the region. Two paths with common endpoints are called homotopic if one can be continuously deformed into the other leaving the end points fixed and remaining within its defined region. In part A of the , the shaded region has a hole in it; f and g are homotopic paths, but g' is not homotopic to f or g since g' cannot be deformed into f or g without passing through the hole and leaving the region

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Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
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