One of the classic theorems concerning the real numbers states that every open cover of a closed and bounded subset of the real line contains a finite subcover. Compactness is an abstraction of that notion, and there are several ideas concerning it which are equivalent and many which are similar. The purpose of this paper is to synthesize the more important of these ideas. This synthesis is accomplished by demonstrating either situations in which two ordinarily different conditions are equivalent or combinations of two or more properties which will guarantee a third.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc130821 |
| Date | 08 1900 |
| Creators | Bell, Wayne Charles |
| Contributors | Cecil, David R., Dawson, David Fleming |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iv, 48 leaves, Text |
| Rights | Public, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved., Bell, Wayne Charles |
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