Let $X$ be a topological space and let $f:X\rightarrow X$ be a continuous self-morphism of topological spaces. Let $Y$ be a closed $f$-stable subset of $X$, that is, suppose $f(Y)\subseteq Y$. Consider the additional condition that $f^{-1}(Y)=Y$. Is there a terminology for this situation in topological dynamics? I am not sure if there exists a terminology for this, but I am tempted to say $f$ ** isolates** $Y$ if:

**1)**$Y$ is $f$-stable, and

**2)**$f^{-1}(Y)=Y$.