On the epireflectivity of the Wallman-Shanin-type compactification for approach spaces

In this paper, we study the functorial behaviour of the Wallman-Shanin-type compactification for weakly symmetric T-1 approach spaces, as defined in (R. Lowen and M. Sioen [13]). We do this by generalizing the technique used by H. L. Bentley and S. A. Naimpally in their paper [2], yielding a recharacterization of our quantified compactification theory in terms of contiguity clusters of [0, infinity]-valued functionals and we also define a construct WS (which is the counterpart of SEP in [2]) on a suitable non-full subconstruct of which the Wallman-Shanin-type compactification determines an epireflection.