Absolute $n$-fold hyperspace suspensions

Tom 105 / 2006

Sergio Macías, Sam B. Nadler, Jr. Colloquium Mathematicum 105 (2006), 221-231 MSC: Primary 54B20; Secondary 54F15. DOI: 10.4064/cm105-2-5

Streszczenie

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.

Autorzy

  • Sergio MacíasInstituto de Matemáticas
    U.N.A.M.
    Circuito Exterior, Ciudad Universitaria
    México D.F., C.P. 04510, México
    e-mail
  • Sam B. Nadler, Jr.Department of Mathematics
    West Virginia University
    P.O. Box 6310
    Morgantown, WV 26506-6310, U.S.A.
    e-mail

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