Omega-limit sets and non-continuous functions (Q5970664)

It is shown that a function has the dense mapping property if and only if it is bilaterally quasicontinuous. Many corollaries of this result are presented as well as a result on fixed points of a Darboux-Baire 1 function on closed intervals. The invariance (with respect to \(f\)) of \( \omega \)-limit sets of the iterates of a quasicontinuous \(f:\mathbb R\to \mathbb R\) is shown provided the \( \omega \)-limit set contains a nonempty open subset.