In topology, two continuous functions from one topological space to another are called homotopic (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 between the two functions. A notable use of homotopy is the definition of hom.....
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http://en.wikipedia.org/wiki/Homotopy
A continuous transformation from one mapping to another. One example is the convex combination: tf(x) + (1-t)
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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 ... [1 related articles]
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http://www.britannica.com/eb/a-z/h/66
A continuous transformation from one path in a topological space to another, or, more generally, of one function to another. Paths connected by a homotopy are called homotopic and are said to be in the same homotopy class. Properties left unchanged by such homotopies are known as homotopy invariants...
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http://www.daviddarling.info/encyclopedia/H/homotopy.html
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.
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https://www.infoplease.com/dictionary/homotopy
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