This dissertation explores geometric measure theory; the first part explores a question posed by Paul Erdös -- Is there a number c > 0 such that if E is a Lebesgue measurable subset of the plane with λ²(E) (planar measure)> c, then E contains the vertices of a triangle with area equal to one? -- other related geometric questions that arise from the topic. In the second part, "we parametrize the theorems from general topology characterizing the continuous images and the homeomorphic images of the Cantor set, C" (abstract, para. 5).
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc330800 |
| Date | 08 1900 |
| Creators | Ingram, John M. (John Michael) |
| Contributors | Mauldin, R. Daniel, Appling, William D. L., Dawson, David Fleming, Bilyeu, Russell Gene |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | ii, 88 leaves : ill., Text |
| Rights | Public, Ingram, John Michael, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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