Partner
Degree Department
Degree Level
91 Matching Results
Results open in a new window/tab.
Results:
1 - 24 of
91
next
Topological Groups
The notion of a topological group follows naturally from a combination of the properties of a group and a topological space. Since a group consists of a set G of elements which may be either finite or infinite and since this is also common to a topological space, a question is opened as to whether or not it is possible to assign a topology to a set of elements which form a group under a certain operation. Now it is possible to assign a topology to any set of elements if no restriction is placed on the topology assigned and hence this study would be of little value from the standpoint of the group itself. If however it is required that the group operation be continuous in the topological space then a very interesting theory is developed.
Date:
May 1960
Creator:
Carry, Laroy Ray
System:
The UNT Digital Library
A Development of the Peano Postulates
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.
Date:
May 1963
Creator:
Peek, Darwin Eugene
System:
The UNT Digital Library
Compact Convex Sets in Linear Topological Spaces
The purpose of this paper is to examine properties of convex sets in linear topological spaces with special emphasis on compact convex sets.
Date:
May 1964
Creator:
Read, David R.
System:
The UNT Digital Library
The Comparability of Cardinals
The purpose of this composition is to develop a rigorous, axiomatic proof of the comparability of the cardinals of infinite sets.
Date:
May 1964
Creator:
Owen, Aubrey P.
System:
The UNT Digital Library
Continuous Solutions of Laplace's Equation in Two Variables
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.
Date:
May 1968
Creator:
Johnson, Wiley A.
System:
The UNT Digital Library
Ideals and Boolean Rings: Some Properties
The purpose of this thesis is to investigate certain properties of rings, ideals, and a special type of ring called a Boolean ring.
Date:
May 1968
Creator:
Hu, Grace Min-Ying Chin
System:
The UNT Digital Library
Solving Linear Programming's Transportation Problem
A special case of the linear programming problem, the transportation problem, is the subject of this thesis. The development of a solution to the transportation problem is based on fundamental concepts from the theory of linear algebra and matrices.
Date:
May 1968
Creator:
Culp, William E.
System:
The UNT Digital Library
Spaces of H-Integrable Functions
In this thesis we consider integrals of a certain class of interval functions. Specifically we consider a nondegenerate number interval [a,b], a real valued function m, defined and nondecreasing on [a,b], and the set Hm, of real valued functions f, defined on [a,b] such that: 1) f(a)=0; 2) for each subinterval [p,q] of [a,b], if m(q)-m(p)=0, then f(q)-f(p)=0; and 3) the set of all sums of the form Σ(Δf)2/Δm for subdivisions D of [a,b] is bounded above.
Date:
May 1968
Creator:
Wittenmyer, Eugene L.
System:
The UNT Digital Library
Existence and Uniqueness Theorems for Nth Order Linear and Nonlinear Integral Equations
The purpose of this paper is to study nth order integral equations. The integrals studied in this paper are of the Riemann type.
Date:
May 1969
Creator:
Hurlbert, Gayle Jene Shultz
System:
The UNT Digital Library
A Genesis for Compact Convex Sets
This paper was written in response to the following question: what conditions are sufficient to guarantee that if a compact subset A of a topological linear space L^3 is not convex, then for every point x belonging to the complement of A relative to the convex hull of A there exists a line segment yz such that x belongs to yz and y belongs to A and z belongs to A? Restated in the terminology of this paper the question bay be given as follow: what conditions may be imposed upon a compact subset A of L^3 to insure that A is braced?
Date:
May 1969
Creator:
Ferguson, Ronald D.
System:
The UNT Digital Library
Algebraic Properties of Semigroups
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.
Date:
May 1971
Creator:
Lumley, Robert Don
System:
The UNT Digital Library
Ideals in Quadratic Number Fields
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.
Date:
May 1971
Creator:
Hamilton, James C.
System:
The UNT Digital Library
Radicals of a Ring
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.
Date:
May 1971
Creator:
Crawford, Phyllis Jean
System:
The UNT Digital Library
Set Function Integrals and Absolute Continuity
The purpose of this thesis is to investigate a theory of integration of real-valued functions defined on fields of sets.
Date:
May 1971
Creator:
Hootman, Robert W.
System:
The UNT Digital Library
Metric Half-Spaces
This paper is a study of some of the basic properties of the metric half-space topology, a topology on a set which is derived from a metric on the set. In the first it is found that in a complete inner product space, the metric half-space topology is the same as one defined in terms of linear functionals on the space. In the second it is proven that in Rn the metric half-space topology is the same as the usual metric topology. In the third theorem it is shown that in a certain sense the nature of the metric halfspace topology generated by a norm on the space determines whether the norm is quadratic, that is to say, whether or not there exists an inner product on the space with the property that |x|^2=(x,x) for all x in the space.
Date:
May 1972
Creator:
Dooley, Willis L.
System:
The UNT Digital Library
Near-Rings
The primary objective of this work is to discuss some of the elementary properties of near-rings as they are related to rings. This study is divided into three subdivisions: (1) Basic Properties and Concepts of Near-Rings; (2) The Ideal Structure of Near-Rings; and (3) Homomorphism and Isomorphism of Near-Rings.
Date:
May 1972
Creator:
Baker, Edmond L.
System:
The UNT Digital Library
The Riemann-Complete Integral
The problem with which this paper is concerned is that of defining the Riemann-Complete Integral and comparing it with the Riemann and the Lebesgue Integrals.
Date:
May 1972
Creator:
Boyd, Eddie
System:
The UNT Digital Library
A*-algebras and Minimal Ideals in Topological Rings
The present thesis mainly concerns B*-algebras, A*-algebras, and minimal ideals in topological rings.
Date:
May 1973
Creator:
Wei, Jui-Hung
System:
The UNT Digital Library
Development of a Geometry from a Set of Axioms
The purpose of this paper is to develop a geometry based on fourteen axioms and four undefined terms.
Date:
May 1973
Creator:
Glasscock, Anita Louise
System:
The UNT Digital Library
Lebesgue-Stieltjes Measure and Integration
The purpose of the thesis is to investigate an approach to Lebesgue-Stieltjes measure and integration.
Date:
May 1973
Creator:
Seale, Laura S.
System:
The UNT Digital Library
R-Modules for the Alexander Cohomology Theory
The Alexander Wallace Spanier cohomology theory associates with an arbitrary topological space an abelian group. In this paper, an arbitrary topological space is associated with an R-module. The construction of the R-module is similar to the Alexander Wallace Spanier construction of the abelian group.
Date:
May 1973
Creator:
Anderson, Stuart Neal
System:
The UNT Digital Library
Euclidean Rings
The cardinality of the set of units, and of the set of equivalence classes of primes in non-trivial Euclidean domains is discussed with reference to the categories "finite" and "infinite." It is shown that no Euclidean domains exist for which both of these sets are finite. The other three combinations are possible and examples are given. For the more general Euclidean rings, the first combination is possible and examples are likewise given. Prime factorization is also discussed in both Euclidean rings and Euclidean domains. For Euclidean rings, an alternative definition of prime elements in terms of associates is compared and contrasted to the usual definitions.
Date:
May 1974
Creator:
Fecke, Ralph Michael
System:
The UNT Digital Library
Absolute Continuity and the Integration of Bounded Set Functions
The first chapter gives basic definitions and theorems concerning set functions and set function integrals. The lemmas and theorems are presented without proof in this chapter. The second chapter deals with absolute continuity and Lipschitz condition. Particular emphasis is placed on the properties of max and min integrals. The third chapter deals with approximating absolutely continuous functions with bounded functions. It also deals with the existence of the integrals composed of various combinations of bounded functions and finitely additive functions. The concluding theorem states if the integral of the product of a bounded function and a non-negative finitely additive function exists, then the integral of the product of the bounded function with an absolutely continuous function exists over any element in a field of subsets of a set U.
Date:
May 1975
Creator:
Allen, John Houston
System:
The UNT Digital Library
Properties of Some Classical Integral Domains
Greatest common divisor domains, Bezout domains, valuation rings, and Prüfer domains are studied. Chapter One gives a brief introduction, statements of definitions, and statements of theorems without proof. In Chapter Two theorems about greatest common divisor domains and characterizations of Bezout domains, valuation rings, and Prüfer domains are proved. Also included are characterizations of a flat overring. Some of the results are that an integral domain is a Prüfer domain if and only if every overring is flat and that every overring of a Prüfer domain is a Prüfer domain.
Date:
May 1975
Creator:
Crawford, Timothy B.
System:
The UNT Digital Library