This paper is a study of continue and related metric spaces, Chapter I is an introductory chapter. Irreducible continua and noncut points are the main topics in Chapter II. The third chapter begins with a few results on locally connected spaces. These results are then used to prove results in locally connected continua. Decomposable and indecomposable continua are dealt with in Chapter IV. Totally disconnected metric spaces are studied in the beginning of Chapter V. Then we see that every compact metric space is a continuous image of the Cantor set. A continuous map from the Cantor set onto [0,1] is constructed. Also, a continuous map from [0,1] onto [0,1]x[0,1] is built, Then an order preserving homeomorphism is constructed from a metric arc onto [0,1],
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc504299 |
| Date | 08 1900 |
| Creators | Brucks, Karen M. (Karen Marie), 1957- |
| Contributors | Hagan, Melvin R., Parrish, Herbert C. |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iv, 73 leaves: ill., Text |
| Rights | Public, Brucks, Karen M. (Karen Marie), 1957-, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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