 n-Fold Hyperspace SuspensionsSergio Macías
Chapter Chapter 7 in Topics on Continua, 2018, pp 327-369 from Springer Abstract: 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. Date: 2018 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-90902-8_7 Ordering information: This item can be ordered from DOI: 10.1007/978-3-319-90902-8_7 Access Statistics for this chapter More chapters in Springer Books from Springer |
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