A -space is a special type of T1-Space. Consider a point and a homeomorphism of an open neighborhood of onto an open set of . Then a space is a -space if, for any two such neighborhoods and , the images of under the different homeomorphisms are isometric. If , the homeomorphisms need only be conformal (but not necessarily orientation-preserving).
Hsiang (2000, p. 1) terms a space with a topological (respectively, differentiable, linear) transformation of a given group a topological (respectively, differentiable, linear) -space.