This paper introduces the background concepts necessary to develop a detailed proof of a theorem by Ralph H. Fox which states that two topological spaces are the same homotopy type if and only if both are deformation retracts of a third space, the mapping cylinder. The concepts of homotopy and deformation are introduced in chapter 2, and retraction and deformation retract are defined in chapter 3. Chapter 4 develops the idea of the mapping cylinder, and the proof is completed. Three special cases are examined in chapter 5.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc504325 |
| Date | 12 1900 |
| Creators | Stark, William D. (William David) |
| Contributors | Hagan, Melvin R., Brand, Neal E., Appling, William D. L. |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iv, 65 leaves : ill., Text |
| Rights | Public, Stark, William D. (William David), Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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