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G-Space


A G-space is a special type of T1-Space. Consider a point x and a homeomorphism of an open neighborhood V of x onto an open set of R^n. Then a space is a G-space if, for any two such neighborhoods v^' and v^(''), the images of v^' union v^('') under the different homeomorphisms are isometric. If n=2, the homeomorphisms need only be conformal (but not necessarily orientation-preserving).

Hsiang (2000, p. 1) terms a space X with a topological (respectively, differentiable, linear) transformation of a given group G a topological (respectively, differentiable, linear) G-space.


See also

Green Space, Schur's Lemma

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References

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

Referenced on Wolfram|Alpha

G-Space

Cite this as:

Weisstein, Eric W. "G-Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/G-Space.html

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