To define the "n"-th homotopy group, the base-point-preserving maps from an "n"-dimensional sphere (with base point) into a given space (with base point) are collected into equivalence classes, called homotopy classes. Two mappings are homotopic if one can be continuously deformed into the other. These homotopy classes form a group, called the "n"-th homotopy group, formula_1, of the given space "X" with base point. Topological spaces with differing homotopy groups are never equivalent (homeomorphic), but topological spaces that "are not" homeomorphic "can" have the same homotopy groups.