A continuous transformation from one function to another. A homotopy between two functions and from a space to a space is a continuous map from such that and , where denotes set pairing. Another way of saying this is that a homotopy is a path in the mapping space from the first function to the second.
Two mathematical objects are said to be homotopic if one can be continuously deformed into the other. The concept of homotopy was first formulated by Poincaré around 1900 (Collins 2004).