Absolute n-fold hyperspace suspensions

Sergio Macías; Sam B. Nadler, Jr.

Colloquium Mathematicae (2006)

  • Volume: 105, Issue: 2, page 221-231
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Sergio Macías, and Sam B. Nadler, Jr.. "Absolute n-fold hyperspace suspensions." Colloquium Mathematicae 105.2 (2006): 221-231. <http://eudml.org/doc/283515>.

@article{SergioMacías2006,
abstract = {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.},
author = {Sergio Macías, Sam B. Nadler, Jr.},
journal = {Colloquium Mathematicae},
keywords = {continuum; dimensionally homogeneous; Hilbert cube manifolds; Peano continua; 2-sphere; unicoherent continuum},
language = {eng},
number = {2},
pages = {221-231},
title = {Absolute n-fold hyperspace suspensions},
url = {http://eudml.org/doc/283515},
volume = {105},
year = {2006},
}

TY - JOUR
AU - Sergio Macías
AU - Sam B. Nadler, Jr.
TI - Absolute n-fold hyperspace suspensions
JO - Colloquium Mathematicae
PY - 2006
VL - 105
IS - 2
SP - 221
EP - 231
AB - 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.
LA - eng
KW - continuum; dimensionally homogeneous; Hilbert cube manifolds; Peano continua; 2-sphere; unicoherent continuum
UR - http://eudml.org/doc/283515
ER -

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