In this paper, spindle starshaped sets are introduced and investigated, which
apart from normalization form an everywhere dense subfamily within the family
of starshaped sets. We focus on proving spindle starshaped analogues of recent
theorems of Bobylev, Breen, Toranzos, and Zamfirescu on starshaped sets.
Finally, we consider the problem of guarding treasures in an art gallery (in
the traditional linear way as well as via spindles).Comment: 16 pages, 2 figure
