Concerning the mutually aposyndetic decomposition of products of homogeneous continua (Q2850636)

A continuum \(X\) is mutually aposyndetic if for every two distinct points \(p, q \in X\) there are two disjoint subcontinua \(A, B \subset X\) such that \(A\) contains \(p\) in its interior and \(B\) contains \(q\) in its interior. In this paper the mutual aposyndesis of products of homogeneous continua is investigated. It is proved that ``the product of a homogeneous mutually aposyndetic continuum and any continuum is mutually aposyndetic.'' Furthemore the author gives ``some conditions for which a product of two homogeneous decomposable continua is mutually aposyndetic. Certain products involving continuous curves of pseudo-arcs are shown to be mutually aposyndetic. In particular, if a product of two solenoids is mutually aposyndetic, related products involving solenoids of pseudo-arcs are shown to be mutually aposyndetic. We also determine the mutually aposyndetic decomposition of a pseudo-arc and certain other homogeneous continua.''