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n-Fold Hyperspace Suspensions

In: Topics on Continua

Author

Listed:
  • Sergio Macías

    (Universidad Nacional Autónoma de México, Instituto de Matemáticas)

Abstract

In 1979 Sam B. Nadler, Jr. introduced the hyperspace suspension of a continuum to present examples of disk-like continua with the fixed point property. We show that the n-fold hyperspace suspension of a continuum has the same dimension as the n-fold hyperspace of the continuum. We prove that n-fold hyperspace suspensions are zero-dimensional aposyndetic. We give sufficient conditions to have the n-fold hyperspace suspensions are contractible. We present results of local connectedness. In particular, we characterize the arc as the only continuum for which its n-fold hyperspace suspensions are cells. We give properties of points that arcwise disconnect these spaces. We present necessary or sufficient conditions in order to have that n-fold hyperspace suspensions are homeomorphic to a cone, suspension or product of continua. We present sufficient conditions to obtain that n-fold hyperspace suspensions have the fixed point property. We study absolute n-fold hyperspace suspensions. We end the chapter proving that hereditarily indecomposable continua have unique n-fold hyerpsace suspensions.

Suggested Citation

  • Sergio Macías, 2018. "n-Fold Hyperspace Suspensions," Springer Books, in: Topics on Continua, edition 2, chapter 0, pages 327-369, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-90902-8_7
    DOI: 10.1007/978-3-319-90902-8_7
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