Homotopy

Natural & Formal Sciences Dictionary
A continuous deformation between two continuous maps (or spaces) parameterized by an interval: a homotopy between maps f and g is a continuous map H(x,t) with H(·,0)=f and H(·,1)=g, encoding that f can be continuously deformed into g.

Homotopy

- Mathematics & Logic -
Pure Mathematics Dictionary
A continuous family of maps F: X × [0,1] → Y interpolating between two continuous maps f0 and f1 (F(·,0)=f0, F(·,1)=f1); it formalizes the notion of deforming one map into another through continuous maps.