More absorbers in hyperspaces
The family of all subcontinua that separate a compact connected $n$-manifold $X$ (with or without boundary), $n\ge 3$, is an $F_σ$-absorber in the hyperspace $C(X)$ of nonempty subcontinua of $X$. If $D_2(F_σ)$ is the small Borel class of spaces which are differences of two $σ$-compact sets, then the family of all $(n-1)$-dimensional continua that separate $X$ is a $D_2(F_σ)$-absorber in $C(X)$. The families of nondegenerate colocally connected or aposyndetic continua in $I^n$ and of at least two-dimensional or decomposable Kelley continua are $F_{σδ}$-absorbers in the hyperspace $C(I^n)$ for $n\ge 3$. The hyperspaces of all weakly infinite-dimensional continua and of $C$-continua of dimensions at least 2 in a compact connected Hilbert cube manifold $X$ are $Π^1_1$-absorbers in $C(X)$. The family of all hereditarily infinite-dimensional compacta in the Hilbert cube $I^ω$ is $Π^1_1$-complete in $2^{I^ω}$.