 
					
					
						G-Space					
				 
				
					
						 المؤلف:  
						Hsiang, W. Y
						 المؤلف:  
						Hsiang, W. Y					
					
						 المصدر:  
						 Lectures on Lie Groups. Singapore: World Scientifi
						 المصدر:  
						 Lectures on Lie Groups. Singapore: World Scientifi					
					
						 الجزء والصفحة:  
						p. 1
						 الجزء والصفحة:  
						p. 1					
					
					
						 2-8-2021
						2-8-2021
					
					
						 1698
						1698					
				 
				
				
				
				
				
				
				
				
				
			 
			
			
				
				G-Space
A  -space is a special type of T1-Space. Consider a point
-space is a special type of T1-Space. Consider a point  and a homeomorphism of an open neighborhood
 and a homeomorphism of an open neighborhood  of
 of  onto an open set of
 onto an open set of  . Then a space is a
. Then a space is a  -space if, for any two such neighborhoods
-space if, for any two such neighborhoods  and
 and  , the images of
, the images of  under the different homeomorphisms are isometric. If
 under the different homeomorphisms are isometric. If  , the homeomorphisms need only be conformal (but not necessarily orientation-preserving).
, 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
 with a topological (respectively, differentiable, linear) transformation of a given group  a topological (respectively, differentiable, linear)
 a topological (respectively, differentiable, linear)  -space.
-space.
REFERENCES:
Hsiang, W. Y. Lectures on Lie Groups. Singapore: World Scientific, p. 1, 2000.
				
				
					
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