homotopy

noun5

1. •
   A continuous deformation of one continuous function or map to another.

   • The concept of homotopy represents a formalisation of the intuitive idea of a smooth deformation of one curve into another.
2. •
   A theory associating a system of groups with each topological space.
3. •
   (informal) Ellipsis of homotopy theory (“the systematic study of homotopies and their equivalence classes”).
4. •
   The relationship between two continuous functions where homotopy from one to the other is evident.
5. •
   A system of groups associated with a topological space.