G-Space

A $G$-space is a special type of Hausdorff Space. Consider a point $x$ and a Homeomorphism of an open Neighborhood $V$ of $x$ onto an Open Set of $\Bbb{R}^n$. Then a space is a $G$-space if, for any two such Neighborhoods $V'$ and $V''$, the images of $V'\cup V''$ under the different Homeomorphisms are Isometric. If $n=2$, the Homeomorphisms need only be conformal (but not necessarily orientation-preserving).

See also Green Space