= Core interval of an expanding tent map
Restrict $T_s(x)=1-s|x|$ to $[-1,1]$, with $1<s\leq2$. Its image is the <closed interval>
$$
A=[1-s,1]=[T_s^2(0),T_s(0)].
$$
Because $0\in A$ and $\max_{x\in A}|x|=1$, its next image is again $T_s(A)=A$. Every state in $[-1,1]$ therefore enters this invariant core after at most one iterate and remains there. This is the core used in <interval exactness of a tent-map core>.
The domain restriction matters. If the same formula defines a <map> on the whole real line, any $x<-1/(s-1)$ stays on the negative branch and satisfies
$$
T_s^n(x)=-\frac1{s-1}+s^n\left(x+\frac1{s-1}\right)\longrightarrow-\infty.
$$
Thus points outside the declared phase interval need not enter $A$, and $A$ is not a globally absorbing interval for the real-line extension.
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