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 ![X×[0,1]|->Y](/images/equations/Homotopy/Inline6.svg)
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).
