Escaping sets are not sigma-compact

Exponential iteration and Borel sets

“…• almost zero-dimensional and cohesive [5,1] • first category and F σδ [5,10] • nowhere G δσ • rim-complete and nowhere rim-σ-compact [6,3] • contains a dense copy of E [7] • each point is contained in a closed copy of E c := {x ∈ ℓ 2 : x n / ∈ Q for all n < ω} [1,6] • cannot be written as a countable union of nowhere dense C-sets. [8] The last property distinguishes Ė(f ) from Q ω and E. It is unknown whether Ė(f ) is a topological group, or is at least homogeneous.…”