Real functions \(f\) defined on the entire plane and depending only on the first coordinate, i.e., \(f(x,y)= f(x)\), are considered. As on the real line such functions can be discontinuous but having the Darboux property.
However, in the paper under review it is shown that, in contrast to the situation on the line, any such \(f\) is in fact continuous if we merely know it to be almost continuous or to be a connectivity function.