A relative Sierpinski theorem. Erratum to: ``Nonhyperbolic Coxeter groups with Menger boundary'' (Q2070056)

Summary: The purpose of this erratum is to correct the proof of Proposition 2.3 of [the authors, ibid. 65, No. 1--2, 207--220 (2019; Zbl 1472.20091)]. A classical theorem of Sierpinski states that every subspace of dimension at most one in the 2-dimensional disc \(D^2\) can be topologically embedded in the Sierpinski carpet. The proof of Proposition 2.3 of [loc. cit.] implicitly provides a relative version of Sierpinski's theorem. Unfortunately the proof of Proposition 2.3 given in [loc. cit.] is incorrect. We provide two brief proofs that each fill this gap. One is a self-contained argument suited specifically for the needs of [loc. cit.], and in the other we explicitly prove a relative embedding theorem that produces embeddings in the Sierpinski carpet with certain prescribed boundary values.