Difference between revisions of "Klein space"
From Encyclopedia of Mathematics
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| − | A topological space on which a group of homeomorphic mappings of the space onto itself is defined, with the property that there exist for any two points | + | A topological space on which a group of homeomorphic mappings of the space onto itself is defined, with the property that there exist for any two points $A$ and $B$ of the space a transformation of this group taking $A$ to $B$. |
The origin of the term "Klein space" is connected with the [[Erlangen program|Erlangen program]] of F. Klein (1872), in which different geometries were defined from the point of view of their corresponding transformation groups. | The origin of the term "Klein space" is connected with the [[Erlangen program|Erlangen program]] of F. Klein (1872), in which different geometries were defined from the point of view of their corresponding transformation groups. | ||
Latest revision as of 19:26, 17 April 2014
homogeneous space
A topological space on which a group of homeomorphic mappings of the space onto itself is defined, with the property that there exist for any two points $A$ and $B$ of the space a transformation of this group taking $A$ to $B$.
The origin of the term "Klein space" is connected with the Erlangen program of F. Klein (1872), in which different geometries were defined from the point of view of their corresponding transformation groups.
Comments
See also Homogeneous space.
References
| [a1] | F. Klein, "The Erlangen program" Math. Intelligencer , 0 (1977) pp. 22–30 |
How to Cite This Entry:
Klein space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Klein_space&oldid=31836
Klein space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Klein_space&oldid=31836
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article