Inverse limits of Čech-Stone compactifications (Q2665206)

A subcontinuum \(W\) of a continuum \(X\) is a continuum neighborhood of \(p \in X\) if \(p\) lies in the interior of \(W\). The continuum \(X\) is mutually aposyndetic if distinct points of \(X\) have disjoint continuum neighborhoods. The author defines an inverse limit \(\Sigma\) of the system of Čech-Stone compactifications of \(S\setminus A\) where \(S\) is a fixed \(n\)-sphere \((n > 1)\) and \(A\) is a finite subset of \(S\). He shows that \(\Sigma\) is mutually aposyndetic and the only metrizable subcontinua are degenerate. Further, \(\Sigma\) admits a montone map onto an \(n\)-sphere such that each point inverse has cardinality \(2^c\). The paper ends with two open questions.