Homeomorphisms with the pseudo orbit tracing property of the Cantor set (Q789798)

Let C be the Cantor set of all real numbers \(x\in [0,1]\) such that \(x=3^{-1}a_ 1+3^{-2}a_ 2+..\). with \(a_ i=0\) or 2 for \(i\geq 1\). We denote by H(C) the set of all homeomorphisms of C and by P(C) the set of all homeomorphisms of C having the pseudo-orbit tracing property. The set H(C) is a complete metric space with respect to the metric d on H(C) defined by \(d(f,g)=\max \{| f(x)-g(x)|\); \(x\in C\}\) for f,\(g\in H(C)\). The author proves the following interesting theorem: P(C) is dense in H(C). For the proof the author uses a result due to \textit{P. Walters} [Lect. Notes Math. 668, 231-244 (1978; Zbl 0403.58019)], which states that a subshift has the pseudo-orbit tracing property if and only if it is of finite type. It is unknown whether the above theorem is true when C is replaced by a compact connected manifold.