G-Space

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.

REFERENCES:

Hsiang, W. Y. Lectures on Lie Groups. Singapore: World Scientific, p. 1, 2000.