More absorbers in hyperspaces

The family of all subcontinua that separate a compact connected n-manifold X (with or without boundary), n≥3, is an Fσ-absorber in the hyperspace C(X) of nonempty subcontinua of X. If D2(Fσ) 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 D2(Fσ)-absorber in C(X). The families of nondegenerate colocally connected or aposyndetic continua in In and of at least two-dimensional or decomposable Kelley continua are Fσδ-absorbers in the hyperspace C(In) for n≥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 Π11-absorbers in C(X). The family of all hereditarily infinite-dimensional compacta in the Hilbert cube Iω is Π11-complete in 2Iω.