Domains of attraction of generic \(\omega\)-limit sets for strongly monotone semiflows (Q1188360)

The asymptotic behaviour and the domain of attraction of a generic \(\omega\)-limit set of a strongly increasing semiflow in a strongly ordered metrizable space \(X\) are investigated. The author shows that if \(X\) is an open and order-convex subset of a separable strongly ordered Banach space then the \(\omega\)-unstable points are contained in the union of at most countably many Lipschitz manifolds of codimension 1. Thus ``almost all'' points are \(\omega\)-stable.