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 ≥ 3 and none when n = 2. Finally, it is shown that infinite-dimensional absolute n-fold hyperspace suspensions must be unicoherent Hilbert cube manifolds.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-2-5,
author = {Sergio Mac\'\i as and Sam B. Nadler, Jr.},
title = {Absolute n-fold hyperspace suspensions},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {221-231},
zbl = {1102.54009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-2-5}
}
Sergio Macías; Sam B. Nadler, Jr. Absolute n-fold hyperspace suspensions. Colloquium Mathematicae, Tome 106 (2006) pp. 221-231. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-2-5/