Spaces such as the closed interval [0, 1] do not have the property of being homogeneous, strongly locally homogeneous (SLH) or countable dense homogeneous (CDH), but the Hilbert cube has all three properties. We investigate subsets X of real numbers to determine when their countable product is homogeneous, SLH, or CDH. We give necessary and sufficient conditions for the product to be homogeneous. We also prove that the product is SLH if and only if X is zero-dimensional or an interval. And finally we show that for a Borel subset X of real numbers the product is CDH iff X is a G-delta zero-dimensional set or an interval.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc1011753 |
| Date | 08 1900 |
| Creators | Allen, Cristian Gerardo |
| Contributors | Gao, Su, Conley, Charles, Sari, Bunyamin |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | v, 75 pages, Text |
| Rights | Public, Allen, Cristian Gerardo, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved. |
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