In this paper we make use of the the concept of covering spaces for homogeneous continua as pioneered by Rogers and refined by Maciaas. For a continuum X embedded essentially into the product of the circle S1 and the Hilbert cube Q , we examine the structure of the space X˜ which is the preimage of X under a standard covering map p : RxQ→S1xQ . We show that the compactification of components of X˜ must be decomposable, and are aposyndetic whenever X is. We also demonstrate the conditions under which higher order forms of aposyndesis are inherited by the components of X˜ as well. We conclude by examining the continuum component structure of X˜ and develop several theorems that allow us to determine the cardinality of the collection of continuum components / acase@tulane.edu
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_27252 |
| Date | January 2011 |
| Contributors | Meddaugh, Jonathan (Author), Moll, Victor (Thesis advisor) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Rights | Access requires a license to the Dissertations and Theses (ProQuest) database., Copyright is in accordance with U.S. Copyright law |
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