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  Partner: UNT Libraries
 Degree Discipline: Mathematics
 Collection: UNT Theses and Dissertations
Uniform Locally Compact Spaces

Uniform Locally Compact Spaces

Date: December 1971
Creator: Page, Perman Hutson
Description: The purpose of this paper is to develop some properties of uniformly locally compact spaces. The terminology and symbology used are the same as those used in General Topology, by J. L. Kelley.
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On Lane's Integral

On Lane's Integral

Date: August 1971
Creator: Hill, William James
Description: The problem and purpose of this paper is to develop Lane's Integral in two-space, and then to expand these concepts into three-space and n-space. Lane's Integral can be used by both mathematicians and statisticians as one of the tools in the calculation of certain probabilities and expectations. The method of presentation is straightforward with the basic concepts of integration theory and Stieltjes Integral assumed.
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Product and Function Spaces

Product and Function Spaces

Date: August 1971
Creator: Barrett, Lewis Elder
Description: In this paper the Cartesian product topology for an arbitrary family of topological spaces and some of its basic properties are defined. The space is investigated to determine which of the separation properties of the component spaces are invariant.
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Rings of Continuous Functions

Rings of Continuous Functions

Date: August 1971
Creator: Connell, Carolyn
Description: The purpose of this paper is to examine properties of the ring C(X) of all complex or real-valued continuous functions on an arbitrary topological space X.
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Some Properties of Valuation Rings

Some Properties of Valuation Rings

Date: August 1971
Creator: Miller, Linda C.
Description: This thesis investigates some of the properties of valuation rings. It is assumed that the reader is familiar with the basic properties of commutative rings and ideals in rings. Unless otherwise stated, all rings considered in this thesis are commutative rings with a unity.
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Algebraic Properties of Semigroups

Algebraic Properties of Semigroups

Date: May 1971
Creator: Lumley, Robert Don
Description: This paper is an algebraic study of selected properties of semigroups. Since a semigroup is a result of weakening the group axioms, all groups are semigroups. One facet of the paper is to demonstrate various semigroup properties that induce the group axioms.
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Ideals in Quadratic Number Fields

Ideals in Quadratic Number Fields

Date: May 1971
Creator: Hamilton, James C.
Description: The purpose of this thesis is to investigate the properties of ideals in quadratic number fields, A field F is said to be an algebraic number field if F is a finite extension of R, the field of rational numbers. A field F is said to be a quadratic number field if F is an extension of degree 2 over R. The set 1 of integers of R will be called the rational integers.
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Radicals of a Ring

Radicals of a Ring

Date: May 1971
Creator: Crawford, Phyllis Jean
Description: The problem with which this investigation is concerned is that of determining the properties of three radicals defined on an arbitrary ring and determining when these radicals coincide. The three radicals discussed are the nil radical, the Jacobsson radical, and the Brown-McCoy radical.
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Set Function Integrals and Absolute Continuity

Set Function Integrals and Absolute Continuity

Date: May 1971
Creator: Hootman, Robert W.
Description: The purpose of this thesis is to investigate a theory of integration of real-valued functions defined on fields of sets.
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Separation Properties

Separation Properties

Date: December 1970
Creator: Garvin, Billy Ray
Description: The problem with which this paper is concerned is that of investigating a class of topological properties commonly called separation properties. A topological space which satisfies only the definition may be very limited in open sets. By use of the separation properties, specific families of open sets can be guaranteed.
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