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**Partner:**UNT Libraries

**Degree Discipline:**Mathematics

**Collection:**UNT Theses and Dissertations

### T-Functions

**Date:**June 1960

**Creator:**Barlow, John Rice

**Description:**The main purpose of this paper is to make a detailed study of a certain class T of complex functions. The functions of the class T have a special mapping property and are meromorphic in every region. As an application of this study, certain elementary functions are defined and studied in terms of a special T-function.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc108077/

### Product and Function Spaces

**Date:**August 1971

**Creator:**Barrett, Lewis Elder

**Description:**In this paper the Cartesian product topology for an arbitrary family of topological spaces and some of its basic properties are defined. The space is investigated to determine which of the separation properties of the component spaces are invariant.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc131391/

### Properties of Order Relations and Certain Partly Ordered Systems

**Date:**June 1961

**Creator:**Barros, David Nicholas

**Description:**The purpose of this paper is to present a study of partly ordered sets. It includes a rigorous development of relations based on the notion of a relation as a set, lattices, and theorems concerning the lattice of subgroups of a group.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc108130/

### Mycielski-Regular Measures

**Date:**August 2011

**Creator:**Bass, Jeremiah Joseph

**Description:**Let μ be a Radon probability measure on M, the d-dimensional Real Euclidean space (where d is a positive integer), and f a measurable function. Let P be the space of sequences whose coordinates are elements in M. Then, for any point x in M, define a function ƒn on M and P that looks at the first n terms of an element of P and evaluates f at the first of those n terms that minimizes the distance to x in M. The measures for which such sequences converge in measure to f for almost every sequence are called Mycielski-regular. We show that the self-similar measure generated by a finite family of contracting similitudes and which up to a constant is the Hausdorff measure in its dimension on an invariant set C is Mycielski-regular.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc84171/

### A Set of Axioms for a Topological Space

**Date:**August 1960

**Creator:**Batcha, Joseph Patrick

**Description:**Axioms for a topological space are generally based on neighborhoods where "neighborhood" is an undefined term. Then, limit points are defined in terms of neighborhoods. However, limit points seem to be the basic concept of a topological space, rather than neighborhoods. For this reason, it will be attempted to state a set of axioms for a topological space, using limit point as the undefined concept, and to delete the idea of neighborhoods from the theory.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc108089/

### The Development of the Natural Numbers by Means of the Peano Postulates

**Date:**1951

**Creator:**Baugh, Orvil Lee

**Description:**This thesis covers the development of the natural numbers by means of the peano postulates.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc96984/

### On Sets and Functions in a Metric Space

**Date:**December 1971

**Creator:**Beeman, Anne L.

**Description:**The purpose of this thesis is to study some of the properties of metric spaces. An effort is made to show that many of the properties of a metric space are generalized properties of R, the set of real numbers, or Euclidean n--space, and are specific cases of the properties of a general topological space.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc131457/

### Lebesgue Linear Measure

**Date:**1940

**Creator:**Beeman, William Edwin

**Description:**This paper discusses the concept of a general definition of measure, and shows that the Lebesgue measure satisfies the requirements set forth for the ideal definition.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc75587/

### 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/

### Restricting Invariants and Arrangements of Finite Complex Reflection Groups

**Date:**August 2015

**Creator:**Berardinelli, Angela

**Description:**Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is a subspace of V. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then restriction defines a homomorphism from the algebra of G-invariant polynomial functions on V to the algebra of C-invariant functions on X. In my thesis, I extend earlier work by Douglass and Röhrle for Coxeter groups to the case where G is a complex reflection group of type G(r,p,n) in the notation of Shephard and Todd and X is in the lattice of the reflection arrangement of G. The main result characterizes when the restriction mapping is surjective in terms of the exponents of G and C and their reflection arrangements.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc804919/