On indecomposable \(\frac {1}{2}\)-homogeneous circle-like continua (Q1928411)

V.~Neumann-Lara, P.~Pellicer-Covarrubias and I.~Puga-Espinosa in one of their papers described a decomposable \(\frac{1}{2}\)-homogeneous circle-like continuum. In the same paper they asked whether there exists an indecomposable \(\frac{1}{2}\)-homogeneous circle-like continuum. In this paper the author gives the answer to the above question. Furthermore, he proves that there is an uncountable family of topologically distinct indecomposable \(\frac{1}{2}\)-homogeneous circle-like continua. His construction of indecomposable \(\frac{1}{2}\)-homogeneous circle-like continua is based on inverse limits of decomposable \(\frac{1}{2}\)-homogeneous circle-like continua. Each factor space is the \(\frac{1}{2}\)-homogeneous \(n\)-fold covering space of a continuum described by V.~Neumann-Lara, P.~Pellicer-Covarrubias and I.~Puga-Espinosa, the bonding maps are the covering maps and the resulting space is a solenoidal continuum. In the end of the paper he proves that for an indecomposable \(\frac{1}{2}\)-homogeneous circle-like continuum \(Y\) the two orbits of Homeo(\(Y\)) are uncountable.