Worlds of David Darling
Encyclopedia of Science
   
Home > Encyclopedia of Science

homotopy




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. Homotopy classes of paths can be composed to form the fundamental group, or first homotopy group. Other maps can be used to form higher homotopy groups.


Related category

   • TOPOLOGY