  We study three possible definitions of the notion of CR functions at CR
singular points, their extension to a fixed-neighborhood of the singular point,
and analogues of the Baouendi-Tr\'eves approximation in a fixed neighborhood.
In particular, given the existence of a large enough disc hull shrinking to a
point, we find the fixed-neighborhood extension and hence approximation
properties. We provide examples showing the distinctions between the classes
and the various properties studied.
