Omega-limit sets in hereditarily locally connected continua (Q929985)

This paper gives a topological characterization of \(\omega\)-limit sets in hereditarily locally connected continua \(X\). For a non-degenerate completely regular continuum \(X\) this reduces to the following: a subset of \(X\) is an \(\omega\)-limit set if and only if it is either a finite union of disjoint non-degenerate subcontinua of \(X\) or a nowhere dense closed subset of \(X\). Orbit-enclosing \(\omega\)-limit sets in such \(X\) are also characterized.