Classifying homogeneous continua (Q1203849)

In [Topology Proc. 8, No. 1, 213-233 (1983; Zbl 0541.54039)] the author proposed a complete classification of homogeneous curves and a possible outline of a proof that all homogeneous continua of dimension \(n>1\) are aposyndetic. In this paper, the classification of homogeneous continua is further addressed by discussing the progress that has been made, and by stating several strategy-implying questions. In particular, the author specifies the conditions under which each homogeneous curve would be (1) a simple curve or a Menger universal curve, (2) the total space of a Cantor set bundle over a type (1) curve, (3) a curve admitting a continuous decomposition into pseudo-arc such that the quotient space is a curve of type (1) or (2), or (4) a pseudo-arc.