Sets which are almost starshaped (Q1266477)

According to [\textit{J. Cel}, J. Geom. 53, No. 1-2, 28-36 (1995; Zbl 0831.52003)], a closed connected nonconvex set \(S\) in \(R^d\) with a bounded subset of local nonconvexity points is starshaped if and only if every \(d+1\) or fewer such points are clearly visible via \(S\) from a common point. An analogous criterion for \(S\) open, connected and nonconvex was established by the author in [Geom. Dedicata 66, No. 3, 293-301 (1997; Zbl 0908.46005)]. In the present paper, the author obtains a characterization of a similar type for sets which are neither closed nor open. This generalizes a planar result by \textit{M. Breen} [Geom. Dedicata 13, 201-213 (1982; Zbl 0511.52004)].