A Hypergroup Dual Space Can be Unbounded

Abstract

Unlike topological groups, hypergroups are not closed under duality. While it has long been known that a hypergroup dual space might be signed, the boundedness of such dual spaces has been an open question. In this paper it is shown that a hypergroup dual space may fail to be bounded. An example will be given of an infinite direct product of finite hypergroups whose dual space is a semi-bounded, but not bounded, generalized hypergroup.