On Darboux asymmetry (Q795940)

For a function f:\(R\to R\), a point \(a\in R\) is said to be a right Darboux point iff \[ c_ 1=\lim \inf_{x\to a+}f(x)\leq f(a)\leq \lim \sup_{x\to a+}f(x)=c_ 2, \] and \(c_ 1<c<c_ 2\), \(\delta>0\) imply the existence of \(x\in(a,a+\delta)\) such that \(f(x)=c\). Left Darboux points are defined similarly. The author shows that the set of those points that are right Darboux points without being left ones is countable.