Homeomorphisms of composants of Knaster continua (Q2773371)

Let \(f_p:[0,1]\rightarrow [0,1]\), \(p\geq 2\), be the piecewise linear continuous map constructed as follows: the set \(E:=\{ i/p: i=0,1,...,p \}\) contains all strictly maximum or minimum of \(f_p\), \(f_p(E)= \{ 0,1\}\), \(f(0)=0\) and \((f_p)| _{[i/p,(i+1)/p]}\) is linear for \(0\leq i<p\). For \(p=2\), the map \(f_2\) is the classical tent map. For any \(p\geq 2\) consider the inverse limit space \(K_p\) defined by \(K_p:= \{ (x_0,x_1,...,x_n,...): f_p(x_i)=x_{i-1},i\geq 1 \} \). This set is an indecomposable continuum with uncountably many arcwise connected components. The component containing the sequence \((0,0,...,0,...)\) will be called the zero component and the one component is those containing the sequence \((1,1,...,1,...)\) (for \(p\) odd). NEWLINENEWLINE\textit{C. Bandt} [Fundam. Math. 144, No. 3, 231--241 (1994; Zbl 0818.54028)] answered a question by Knaster proving that all non-zero components of \(K_2\) are homeomorphic. The author generalizes Bandt's result for \(K_p\). More precisely, he proves that the components of \(K_p\) different from the zero and one components are homeomorphic.