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  Partner: UNT Libraries
 Degree Discipline: Mathematics
 Collection: UNT Theses and Dissertations
A Generalization of the Weierstrass Approximation Theorem

A Generalization of the Weierstrass Approximation Theorem

Date: August 1972
Creator: Murchison, Jo Denton
Description: A presentation of the Weierstrass approximation theorem and the Stone-Weierstrass theorem and a comparison of these two theorems are the objects of this thesis.
Contributing Partner: UNT Libraries
Integration of Vector Valued Functions

Integration of Vector Valued Functions

Date: August 1972
Creator: Anderson, Edmond Cardell, III
Description: This paper develops an integral for Lebesgue measurable functions mapping from the interval [0, 1] into a Banach space.
Contributing Partner: UNT Libraries
The Lp Spaces of Equivalence Classes of Lebesgue Integrable Functions

The Lp Spaces of Equivalence Classes of Lebesgue Integrable Functions

Date: August 1972
Creator: Peel, Jerry
Description: The purpose of the paper is to prove that the Lp spaces, p ≥ 1, of equivalence classes of functions are Banach spaces.
Contributing Partner: UNT Libraries
On the Stielitjes Integral

On the Stielitjes Integral

Date: August 1972
Creator: Keagy, Thomas A.
Description: This paper is a study of the Stieltjes integral, a generalization of the Riemann integral normally studied in introductory calculus courses. The purpose of the paper is to investigate many of the basic manipulative properties of the integral.
Contributing Partner: UNT Libraries
Metric Half-Spaces

Metric Half-Spaces

Date: May 1972
Creator: Dooley, Willis L.
Description: 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.
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Near-Rings

Near-Rings

Date: May 1972
Creator: Baker, Edmond L.
Description: 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.
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The Riemann-Complete Integral

The Riemann-Complete Integral

Date: May 1972
Creator: Boyd, Eddie
Description: 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.
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Completeness Axioms in an Ordered Field

Completeness Axioms in an Ordered Field

Date: December 1971
Creator: Carter, Louis Marie
Description: The purpose of this paper was to prove the equivalence of the following completeness axioms. This purpose was carried out by first defining an ordered field and developing some basic theorems relative to it, then proving that lim [(u+u)*]^n = z (where u is the multiplicative identity, z is the additive identity, and * indicates the multiplicative inverse of an element), and finally proving the equivalence of the five axioms.
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The Fundamental Group of Certain Toplogical Spaces

The Fundamental Group of Certain Toplogical Spaces

Date: December 1971
Creator: Hopkins, Billy L.
Description: The problem confronted in this thesis is that of determining direct calculations of the fundamental group of certain topological spaces.
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Inequalities and Set Function Integrals

Inequalities and Set Function Integrals

Date: December 1971
Creator: Milligan, Kenneth Wayne
Description: This thesis investigates some inequalities and some relationships between function properties and integral properties.
Contributing Partner: UNT Libraries