Incomparable compactifications of the ray with Peano continuum as remainder (Q290621)

The authors seek incomparable compactifications \(\alpha H\) of the ray \(H=[0,\infty)\) having a prescribed remainder \(\alpha H-H\), where incomparable means there is no continuous surjection from one onto the other. Given an arbitrary nondegenerate Peano continuum \(X\), the authors construct a family, with cardinality of the continuum, of incomparable compactifications of the ray with \(X\) as remainder. They carefully document and build on the historical development of the problem.