Complete Ordered Fields

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Description

The purpose of this thesis is to study the concept of completeness in an ordered field. Several conditions which are necessary and sufficient for completeness in an ordered field are examined. In Chapter I the definitions of a field and an ordered field are presented and several properties of fields and ordered fields are noted. Chapter II defines an Archimedean field and presents several conditions equivalent to the Archimedean property. Definitions of a complete ordered field (in terms of a least upper bound) and the set of real numbers are also stated. Chapter III presents eight conditions which are equivalent ... continued below

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iv, 73 leaves: ill.

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Arnold, Thompson Sharon August 1977.

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  • Arnold, Thompson Sharon

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Description

The purpose of this thesis is to study the concept of completeness in an ordered field. Several conditions which are necessary and sufficient for completeness in an ordered field are examined. In Chapter I the definitions of a field and an ordered field are presented and several properties of fields and ordered fields are noted. Chapter II defines an Archimedean field and presents several conditions equivalent to the Archimedean property. Definitions of a complete ordered field (in terms of a least upper bound) and the set of real numbers are also stated. Chapter III presents eight conditions which are equivalent to completeness in an ordered field. These conditions include the concepts of nested intervals, Dedekind cuts, bounded monotonic sequences, convergent subsequences, open coverings, cluster points, Cauchy sequences, and continuous functions.

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iv, 73 leaves: ill.

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  • August 1977

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  • May 10, 2015, 6:16 a.m.

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  • June 21, 2016, 3:12 p.m.

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Arnold, Thompson Sharon. Complete Ordered Fields, thesis, August 1977; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc504449/: accessed July 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .