Geodesic
Absolute $n$-fold hyperspace suspensions
Sergio Macías1 ; Sam B. Nadler, Jr.2
1 Instituto de Matemáticas U.N.A.M. Circuito Exterior, Ciudad Universitaria México D.F., C.P. 04510, México
2 Department of Mathematics West Virginia University P.O. Box 6310 Morgantown, WV 26506-6310, U.S.A.
Colloquium Mathematicum, Tome 105 (2006) no. 2, pp. 221-231 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $n\geq 3$ and none when $n=2$. Finally, it is shown that infinite-dimensional absolute $n$-fold hyperspace suspensions must be unicoherent Hilbert cube manifolds.
DOI : 10.4064/cm105-2-5
Keywords: notion absolute n fold hyperspace suspension introduced proved these hyperspaces unicoherent peano continua dimensionally homogeneous shown sphere only finite dimensional absolute fold hyperspace suspension furthermore shown there only possible finite dimensional absolute n fold hyperspace suspensions each geq none finally shown infinite dimensional absolute n fold hyperspace suspensions unicoherent hilbert cube manifolds

Sergio Macías 1 ; Sam B. Nadler, Jr. 2

1 Instituto de Matemáticas U.N.A.M. Circuito Exterior, Ciudad Universitaria México D.F., C.P. 04510, México
2 Department of Mathematics West Virginia University P.O. Box 6310 Morgantown, WV 26506-6310, U.S.A. 
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Sergio Macías; Sam B. Nadler, Jr. Absolute $n$-fold hyperspace suspensions. Colloquium Mathematicum, Tome 105 (2006) no. 2, pp. 221-231. doi: 10.4064/cm105-2-5

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