Compactness and Equivalent Notions

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Description

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.

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iv, 48 leaves

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Bell, Wayne Charles August 1967.

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This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 64 times . More information about this thesis can be viewed below.

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  • Bell, Wayne Charles

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Description

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.

Physical Description

iv, 48 leaves

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UNT Theses and Dissertations

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  • August 1967

Added to The UNT Digital Library

  • Dec. 27, 2012, 10:03 p.m.

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  • Aug. 2, 2013, 3:34 p.m.

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Citations, Rights, Re-Use

Bell, Wayne Charles. Compactness and Equivalent Notions, thesis, August 1967; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc130821/: accessed September 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .