Abstract
This paper introduces a notion of equivalence that links closed relations and quasicontinuous functions; we examine classes of quasicontinuous functions that have the same set of continuity points. In doing so, we show that every minimal closed relation is the closure of a quasicontinuous function and vice-versa. We also show that this notion is of use in dynamical systems. Every quasicontinuous function is equivalent to one that is measurable, and under certain circumstances---in fact, under just those circumstances that appear most often in the dynamics literature---it is equivalent to a quasicontinuous function that has an invariant measure.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have