An internal characterisation of radiality (Q741410)

Radial spaces, first introduced by Horst Herrlich in 1967, are characterised as the pseudo-open images of linearly ordered topological spaces (LOTS). In the present paper, the author provides an internal characterisation of radial spaces in terms of a type of neighbourhood base generated by subspaces that have well-ordered neighbourhood bases at the point in question. For that he introduces a new (hereditary) subclass of radial spaces, called \textit{independently-based spaces}, that have neighbourhoods generated by nests in an appropriate way. This class contains all LOTS, all generalised ordered spaces and all spaces with well-ordered neighbourhood bases (e.g., first-countable spaces).