Absolute $n$-fold hyperspace suspensions
The notion of an absolute $n$-fold hyperspace suspension is introduced. It is proved that these hyperspaces are unicoherent Peano continua and are dimensionally homogeneous. It is shown that the $2$-sphere is the only finite-dimensional absolute $1$-fold hyperspace suspension. Furthermore, it is shown that there are only two possible finite-dimensional absolute $n$-fold hyperspace suspensions for each $n\geq 3$ and none when $n=2$. Finally, it is shown that infinite-dimensional absolute $n$-fold hyperspace suspensions must be unicoherent Hilbert cube manifolds.