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:

• $f$ 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 $f$

Title	stable subspace
Canonical name	StableSubspace
Date of creation	2013-03-22 17:56:52
Last modified on	2013-03-22 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