noun: (topology) A continuous deformation of one continuous function or map to another.
noun: (uncountable) The relationship between two continuous functions where homotopy from one to the other is evident.
noun: (topology) A theory associating a system of groups with each topological space.
noun: (topology) A system of groups associated with a topological space.
noun: (informal) Ellipsis of homotopy theory. (the systematic study of homotopies and their equivalence classes). [(mathematics) The systematic study of the situation of maps' having a homotopy between them; the study of equivalence classes (called homotopy classes) of maps.]
