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stable subspace (Definition)

A subset $ S$ of a larger set $ T$ is said to a stable subset for a function $ f: T\to T$ iff $ f(S)\subset S$.
Alternative phrasings with the same meaning are:

  • $ f$ is an invariant subset for $ f$
  • $ f$ stabilizes $ S$
  • $ S$ is stable under (the action of) $ f$
  • $ S$ is invariant under (the action of) $ f$
  • $ S$ is left stable by/under $ f$
  • $ S$ is left invariant by/under $ f$



"stable subspace" is owned by lalberti.
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Other names:  invariant subspace, stable subset, invariant subset
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Cross-references: invariant, action, stable, function, subset
There are 8 references to this entry.

This is version 3 of stable subspace, born on 2008-03-26, modified 2008-03-27.
Object id is 10446, canonical name is Stable4.
Accessed 240 times total.

Classification:
AMS MSC: 00A05 (General :: General and miscellaneous specific topics :: General mathematics)
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