symmetric set
Definition A subset of a group is said to be symmetric if , where . In other , is symmetric if whenever .
If is a subset of a vector space, then is said to be symmetric if it is symmetric with respect to the additive group structure of the vector space; that is, if [1].
0.0.1 Examples
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1.
In , examples of symmetric sets are intervals of the type with , and the sets and .
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2.
Any vector subspace in a vector space is a symmetric set.
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3.
If is any subset of a group, then and are symmetric sets.
References
- 1 R. Cristescu, Topological vector spaces, Noordhoff International Publishing, 1977.
- 2 W. Rudin, Functional Analysis, McGraw-Hill Book Company, 1973.
Title | symmetric set |
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Canonical name | SymmetricSet |
Date of creation | 2013-03-22 13:48:26 |
Last modified on | 2013-03-22 13:48:26 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 7 |
Author | Koro (127) |
Entry type | Definition |
Classification | msc 20A99 |
Classification | msc 22A05 |
Classification | msc 15-00 |
Classification | msc 46-00 |