homotopy

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.

An integer M is called an exponent for the torsion of an abelian group G if M * (torsion of G) = 0. We say that M is a homotopy exponent for a space X if M is an exponent for πₖ (X) for all k.

The relationship between two continuous functions where homotopy from one to the other is evident.

Ellipsis of homotopy theory (“the systematic study of homotopies and their equivalence classes”).

A theory associating a system of groups with each topological space.

A system of groups associated with a topological space.