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Linear Transformations in Linear Spaces

Description: This thesis is a study of linear spaces and linear transformations in normed linear spaces. The notion of a field, in particular the complex number field, is assumed in this paper.
Date: August 1962
Creator: Westley, Kent N.
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Ordered Triples

Description: The purpose of this paper is the investigation of various properties of ordered triples whose components are elements of certain sets.
Date: August 1962
Creator: Monozingo, Montie Gene
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A Relation for Point Sets in a Topological Space

Description: The purpose of this thesis is to investigate the relation Z for point sets in a topological space. There were two original goals which caused the study.
Date: August 1962
Creator: Warndof, Joseph C.
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Plane Curves

Description: The purpose of this thesis is to present a definition and some properties of a curved arc in a plane and to present a definition and some properties of the Jordan curve.
Date: January 1963
Creator: Heflin, Billy M.
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A Development of the Peano Postulates

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 p… more
Date: May 1963
Creator: Peek, Darwin Eugene
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Additive Functions

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).
Date: June 1963
Creator: McNeir, Ridge W.
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Comparison of Some Mappings in Topology

Description: The main purpose of this paper is the study of transformations in topological space and relationships between special types of transformations.
Date: January 1964
Creator: Aslan, Farhad
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The Solution of Equations in Integers

Description: This paper is devoted to finding integral solutions of algebraic equations. Only algebraic equations with integral coefficients are considered. The elementary properties of integers are assumed.
Date: January 1964
Creator: Read, Billy D.
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Compact Convex Sets in Linear Topological Spaces

Description: 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.
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The Comparability of Cardinals

Description: 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.
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Compact Topological Spaces

Description: The purpose of this paper is to investigate some properties of compact topological spaces and to relate these concepts to the separation properties.
Date: June 1964
Creator: Conway, Thomas M.
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An Approximate Solution to the Dirichlet Problem

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.
Date: August 1964
Creator: Redwine, Edward William
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Metric Postulates for Plane Geometry

Description: The purpose of this paper is to investigate Saunders MacLane's axioms for plane geometry. The wording of the axioms has been modified; however, the concept suggested by each axiom remains the same.
Date: August 1964
Creator: Mahaffy, Donald L.
open access

Some Properties of Metric Spaces

Description: The study of metric spaces is closely related to the study of topology in that the study of metric spaces concerns itself, also, with sets of points and with a limit point concept based on a function which gives a "distance" between two points. In some topological spaces it is possible to define a distance function between points in such a way that a limit point of a set in the topological sense is also a limit point of the same set in a metric sense. In such a case the topological space is "me… more
Date: August 1964
Creator: Brazile, Robert P.
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Some Properties of Rings and Ideals

Description: The purpose of this paper will be to investigate certain properties of algebraic systems known as rings.
Date: August 1964
Creator: Higgins, Jere B.
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Equivalence Classes of Cauchy Sequences of Rational Numbers

Description: The purpose of this thesis is to define equivalence classes of Cauchy sequences of rational numbers and the operations of taking a sum and a product and then to show that this system is an uncountable, ordered, complete field. In so doing, a mathematical system is obtained which is isomorphic to the real number system.
Date: January 1965
Creator: Darnell, Linda Jane
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Ideals in Semigroups

Description: This thesis investigates ideals in semigroups.
Date: January 1965
Creator: Rodgers, Samuel A.
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Pseudo-groups

Description: This thesis examines pseudo-groups and complex groupable lattices.
Date: January 1965
Creator: Weitner, W. Cleo
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Sequences of Real Numbers

Description: The purpose of this thesis is to examine general properties, convergence, and limit points of sequences of real numbers.
Date: January 1965
Creator: Eskew, Mark F.
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Concerning linear spaces

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."
Date: June 1965
Creator: Gilbreath, Joe
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Automorphism Groups

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.
Date: August 1965
Creator: Edwards, Donald Eugene
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The Convolution Ring

Description: This paper deals with the development of the convolution ring and the construction of a field from this ring.
Date: August 1965
Creator: McCormick, Robert E.
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The Laplace Transformation

Description: A set of definitions, theorems and proofs to describe the Laplace transformation.
Date: August 1965
Creator: Floyd, Russell
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