stable subspace
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:

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$f$ is an invariant subset for $f$

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$f$ stabilizes $S$

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$S$ is stable under (the action of) $f$

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$S$ is invariant under (the action of) $f$

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$S$ is left stable by/under $f$

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$S$ is left invariant by/under $f$
Title  stable subspace 

Canonical name  StableSubspace 
Date of creation  20130322 17:56:52 
Last modified on  20130322 17:56:52 
Owner  lalberti (18937) 
Last modified by  lalberti (18937) 
Numerical id  6 
Author  lalberti (18937) 
Entry type  Definition 
Classification  msc 00A05 
Synonym  invariant subspace 
Synonym  stable subset 
Synonym  invariant subset 