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**Partner:**UNT Libraries

**Decade:**1960-1969

**Degree Discipline:**Mathematics

**Collection:**UNT Theses and Dissertations

### Abstract Vector Spaces and Certain Related Systems

**Date:**August 1961

**Creator:**Goddard, Alton Ray

**Description:**The purpose of this paper is to make a detailed study of vector spaces and a certain vector-like system.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc130465/

### Additive Functions

**Date:**June 1963

**Creator:**McNeir, Ridge W.

**Description:**The purpose of this paper is the analysis of functions of real numbers which have a special additive property, namely, f(x+y) = f(x)+f(y).

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc108204/

### Algebraic Integers

**Date:**August 1969

**Creator:**Black, Alvin M.

**Description:**The primary purpose of this thesis is to give a substantial generalization of the set of integers Z, where particular emphasis is given to number theoretic questions such as that of unique factorization. The origin of the thesis came from a study of a special case of generalized integers called the Gaussian Integers, namely the set of all complex numbers in the form n + mi, for m,n in Z. The main generalization involves what are called algebraic integers.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc131119/

### An Approximate Solution to the Dirichlet Problem

**Date:**August 1964

**Creator:**Redwine, Edward William

**Description:**In the category of mathematics called partial differential equations there is a particular type of problem called the Dirichlet problem. Proof is given in many partial differential equation books that every Dirichlet problem has one and only one solution. The explicit solution is very often not easily determined, so that a method for approximating the solution at certain points becomes desirable. The purpose of this paper is to present and investigate one such method.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130550/

### Automorphism Groups

**Date:**August 1965

**Creator:**Edwards, Donald Eugene

**Description:**This paper will be concerned mainly with automorphisms of groups. The concept of a group endomorphism will be used at various points in this paper.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130613/

### Basic Fourier Transforms

**Date:**January 1962

**Creator:**Cumbie, James Randolph

**Description:**The purpose of this paper is to develop some of the more basic Fourier transforms which are the outgrowth of the Fourier theorem. Although often approached from the stand-point of the series, this paper will approach the theorem from the standpoint of the integral.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130482/

### Compact Convex Sets in Linear Topological Spaces

**Date:**May 1964

**Creator:**Read, David R.

**Description:**The purpose of this paper is to examine properties of convex sets in linear topological spaces with special emphasis on compact convex sets.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc130516/

### Compact Topological Spaces

**Date:**June 1964

**Creator:**Conway, Thomas M.

**Description:**The purpose of this paper is to investigate some properties of compact topological spaces and to relate these concepts to the separation properties.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130506/

### Compactness and Equivalent Notions

**Date:**August 1967

**Creator:**Bell, Wayne Charles

**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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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130821/

### The Comparability of Cardinals

**Date:**May 1964

**Creator:**Owen, Aubrey P.

**Description:**The purpose of this composition is to develop a rigorous, axiomatic proof of the comparability of the cardinals of infinite sets.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130514/

### Comparison of Some Mappings in Topology

**Date:**January 1964

**Creator:**Aslan, Farhad

**Description:**The main purpose of this paper is the study of transformations in topological space and relationships between special types of transformations.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc108253/

### Completely Simple Semigroups

**Date:**August 1968

**Creator:**Barker, Bruce W.

**Description:**The purpose of this thesis is to explore some of the characteristics of 0-simple semigroups and completely 0-simple semigroups.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130974/

### Concerning linear spaces

**Date:**June 1965

**Creator:**Gilbreath, Joe

**Description:**The basis for this thesis is H. S. Wall's book, Creative Mathematics, with particular emphasis on the chapter in that book entitled "More About Linear Spaces."

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130586/

### Concerning the Convergence of Some Nets

**Date:**August 1964

**Creator:**Shaw, Jack V.

**Description:**This thesis discusses the convergence of nets through a series of theorems and proofs.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130552/

### Connectedness and Some Concepts Related to Connectedness of a Topological Space

**Date:**August 1969

**Creator:**Wallace, Michael A.

**Description:**The purpose of this thesis is to investigate the idea of topological "connectedness" by presenting some of the basic ideas concerning connectedness along with several related concepts.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc163958/

### Continued Fractions

**Date:**January 1966

**Creator:**Smith, Harold Kermit, Jr.

**Description:**The purpose of this paper is to study convergence of certain continued fractions.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130672/

### Continuous Solutions of Laplace's Equation in Two Variables

**Date:**May 1968

**Creator:**Johnson, Wiley A.

**Description:**In mathematical physics, Laplace's equation plays an especially significant role. It is fundamental to the solution of problems in electrostatics, thermodynamics, potential theory and other branches of mathematical physics. It is for this reason that this investigation concerns the development of some general properties of continuous solutions of this equation.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130948/

### Convergence Preserving Matrices

**Date:**August 1961

**Creator:**Line, Harrell Harvey

**Description:**This paper is the result of a study of triangular matrices with particular emphasis on those which are convergence preserving transformations.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130470/

### Convergence Properties of Filters and Nets

**Date:**August 1968

**Creator:**Price, Joel D.

**Description:**The development of the concept of a filter leads to a theory of convergence in topological spaces. There is a close relationship between the concept of a net and that of a filter.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc131023/

### The Convolution Ring

**Date:**August 1965

**Creator:**McCormick, Robert E.

**Description:**This paper deals with the development of the convolution ring and the construction of a field from this ring.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130633/

### Coverings of Topological Spaces and Paracompactness

**Date:**August 1968

**Creator:**King, Ronald Scott

**Description:**This paper will be devoted to an exposition of some of the basic properties of paracompact spaces. In particular, it will be shown that every pseudo-metrizable space is paracompact and countably paracompact.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc131007/

### A Development of the Peano Postulates

**Date:**May 1963

**Creator:**Peek, Darwin Eugene

**Description:**The purpose of this paper is to develop the Peano postulates from a weaker axiom system than the system used by John L. Kelley in General Topology. The axiom of regularity which states "If X is a non-empty set, then there is a member Y of X such that the intersection of X and Y is empty." is not assumed in this thesis. The axiom of amalgamation which states "If X is a set, then the union of the elements of X is a set." is also not assumed. All other axioms used by Kelley relevant to the Peano postulates are assumed. The word class is never used in the thesis, though the variables can be interpreted as classes.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc108207/

### A Development of the Real Number System

**Date:**August 1961

**Creator:**Matthews, Ronald Louis

**Description:**The purpose of this paper is to construct the real number system. The foundation upon which the real number system will be constructed will be the system of counting numbers.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc130475/

### Differentiable Functions

**Date:**June 1966

**Creator:**McCool, Kenneth B.

**Description:**The primary purpose of this thesis is to carefully develop and prove some of the fundamental, classical theorems of the differential calculus for functions of two real variables.

**Contributing Partner:**UNT Libraries

**Permallink:**digital.library.unt.edu/ark:/67531/metadc130691/