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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
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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 2497 times total.

Classification:
AMS MSC00A05 (General :: General and miscellaneous specific topics :: General mathematics)

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