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  Partner: UNT Libraries
 Department: Department of Mathematics
 Collection: UNT Theses and Dissertations
Schwarz Differentiability

Schwarz Differentiability

Date: August 1968
Creator: Young, William G.
Description: The primary purpose of this paper is to develop a rigorous study of the Schwarz derivative. This study will be based primarily on the comparison of the ordinary derivative to the Schwarz derivative.
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Semitopological Groups

Semitopological Groups

Date: December 1971
Creator: Scroggs, Jack David
Description: This thesis is a study of semitopological groups, a similar but weaker notion than that of topological groups. It is shown that all topological groups are semitopological groups but that the converse is not true. This thesis investigates some of the conditions under which semitopological groups are, in fact, topological groups. It is assumed that the reader is familiar with basic group theory and topology.
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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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Pseudo-groups

Pseudo-groups

Date: January 1965
Creator: Weitner, W. Cleo
Description: This thesis examines pseudo-groups and complex groupable lattices.
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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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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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Properties of Limit Functions

Properties of Limit Functions

Date: December 1972
Creator: Coppin, Anthony M.
Description: The purpose of this paper is to investigate properties of functions which are limits of functions with prescribed properties. Chapter II asks the question "Does a function which is the limit of a sequence of functions each of which is endowed with a certain property necessarily have that property?"
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G-domains, G-ideals, and Hilbert Rings

G-domains, G-ideals, and Hilbert Rings

Date: August 1972
Creator: Draper, Ruben P.
Description: The problem with which this investigation is concerned is that of determining the properties of the following: a particular type of integral domain, the G-domain; a type of prime ideal, the G-ideal; and a special type of ring, the Hilbert ring.
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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.
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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.
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