UNT Theses and Dissertations - 464 Matching Results

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Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces

Description: In the study of Banach spaces, the development of some key properties require studying topologies on the collection of closed convex subsets of the space. The subcollection of closed linear subspaces is studied under the relative slice topology, as well as a class of topologies similar thereto. It is shown that the collection of closed linear subspaces under the slice topology is homeomorphic to the collection of their respective intersections with the closed unit ball, under the natural mapp… more
Date: August 2011
Creator: Farmer, Matthew Ray
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A Study of Functions on Metric Spaces

Description: This thesis describes various forms of metric spaces and establishes some of the properties of functions defined on metric spaces. No attempt is made in this paper to examine a particular type of function in detail. Instead, some of properties of several kinds of functions will be observed as the functions are defined on various forms of metric spaces such as connected spaces, compact spaces, complete spaces, etc.
Date: January 1968
Creator: Brice, Richard S.
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The Study of Translation Equivalence on Integer Lattices

Description: This paper is a contribution to the study of countable Borel equivalence relations on standard Borel spaces. We concentrate here on the study of the nature of translation equivalence. We study these known hyperfinite spaces in order to gain insight into the approach necessary to classify certain variables as either being hyperfinite or not. In Chapter 1, we will give the basic definitions and examples of spaces used in this work. The general construction of marker sets is developed in this wor… more
Date: August 2003
Creator: Boykin, Charles Martin
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Subdirectly Irreducible Semigroups

Description: Definition 1.1. The ordered pair (S,*) is a semi-group iff S is a set and * is an associative binary operation (multiplication) on S. Notation. A semigroup (S,*) will ordinarily be referred to by the set S, with the multiplication understood. In other words, if (a,b)e SX , then *[(a,b)] = a*b = ab. The proof of the following proposition is found on p. 4 of Introduction to Semigroups, by Mario Petrich. Proposition 1.2. Every semigroup S satisfies the general associative law.
Date: December 1978
Creator: Winton, Richard Alan
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Sufficient Conditions for Uniqueness of Positive Solutions and Non Existence of Sign Changing Solutions for Elliptic Dirichlet Problems

Description: In this paper we study the uniqueness of positive solutions as well as the non existence of sign changing solutions for Dirichlet problems of the form $$\eqalign{\Delta u + g(\lambda,\ u) &= 0\quad\rm in\ \Omega,\cr u &= 0\quad\rm on\ \partial\Omega,}$$where $\Delta$ is the Laplace operator, $\Omega$ is a region in $\IR\sp{N}$, and $\lambda>0$ is a real parameter. For the particular function $g(\lambda,\ u)=\vert u\vert\sp{p}u+\lambda$, where $p={4\over N-2}$, and $\Omega$ is the unit ball in $… more
Date: August 1995
Creator: Hassanpour, Mehran
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Sufficient Criteria for Total Differentiability of a Real Valued Function of a Complex Variable in Rn an Extension of H. Rademacher's Result for R²

Description: This thesis provides sufficient conditions for total differentiability almost everywhere of a real-valued function of a complex variable defined on a bounded region in IRn. This thesis extends H. Rademacher's 1918 results in IR2 which culminated in total differentiability, to IRn
Date: August 1982
Creator: Matovsky, Veron Rodieck
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Tauberian Theorems for Certain Regular Processes

Description: In 1943 R. C. Buck showed that a sequence x is convergent if some regular matrix sums every subsequence of x. Thus, for example, if every subsequence of x is Cesaro summable, then x is actually convergent. Buck's result was quite surprising, since research in summability theory up to that time gave no hint of such a remarkable theorem. The appearance of Buck's result in the Bulletin of the American Mathematical Society (3) created immediate interest and has prompted considerable research which … more
Date: August 1975
Creator: Keagy, Thomas A.
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Tensor Products of Banach Spaces

Description: Tensor products of Banach Spaces are studied. An introduction to tensor products is given. Some results concerning the reciprocal Dunford-Pettis Property due to Emmanuele are presented. Pelczyriski's property (V) and (V)-sets are studied. It will be shown that if X and Y are Banach spaces with property (V) and every integral operator from X into Y* is compact, then the (V)-subsets of (X⊗F)* are weak* sequentially compact. This in turn will be used to prove some stronger convergence results for … more
Date: August 1996
Creator: Ochoa, James Philip
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Theory and Methods in Determining the Eigenvalues and Eigenvectors of a Matrix

Description: In the numerous problems of matrix algebra, one finds the problem of determining the eigenvalues of eigenvectors of a matrix quite frequently. The theory and methods leading to the solution of the eigenvalue and eigenvector problem are of considerable interest. The relation between vector spaces, matrices, eigenvalues, and eigenvectors is to be considered in this chapter, with particular concentration directed toward the eigenvalues and eigenvectors shall be developed in the following chapter… more
Date: August 1965
Creator: Waldon, Jerry Herschel
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Thermodynamical Formalism

Description: Thermodynamical formalism is a relatively recent area of pure mathematics owing a lot to some classical notions of thermodynamics. On this thesis we state and prove some of the main results in the area of thermodynamical formalism. The first chapter is an introduction to ergodic theory. Some of the main theorems are proved and there is also a quite thorough study of the topology that arises in Borel probability measure spaces. In the second chapter we introduce the notions of topological pressu… more
Date: August 2004
Creator: Chousionis, Vasileios
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Three Topics in Descriptive Set Theory

Description: This dissertation deals with three topics in descriptive set theory. First, the order topology is a natural topology on ordinals. In Chapter 2, a complete classification of order topologies on ordinals up to Borel isomorphism is given, answering a question of Benedikt Löwe. Second, a map between separable metrizable spaces X and Y preserves complete metrizability if Y is completely metrizable whenever X is; the map is resolvable if the image of every open (closed) set in X is resolvable in Y. I… more
Date: May 2010
Creator: Kieftenbeld, Vincent
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Topics in Category Theory

Description: The purpose of this paper is to examine some basic topics in category theory. A category consists of a class of mathematical objects along with a morphism class having an associative composition. The paper is divided into two chapters. Chapter I deals with intrinsic properties of categories. Various "sub-objects" and properties of morphisms are defined and examples are given. Chapter II deals with morphisms between categories called functors and the natural transformations between functors. Spe… more
Date: August 1974
Creator: Miller, Robert Patrick
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Topological Conjugacy Relation on the Space of Toeplitz Subshifts

Description: We proved that the topological conjugacy relation on $T_1$, a subclass of Toeplitz subshifts, is hyperfinite, extending Kaya's result that the topological conjugate relation of Toeplitz subshifts with growing blocks is hyperfinite. A close concept about the topological conjugacy is the flip conjugacy, which has been broadly studied in terms of the topological full groups. Particularly, we provided an equivalent characterization on Toeplitz subshifts with single hole structure to be flip invari… more
Date: August 2022
Creator: Yu, Ping
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Topological Groups

Description: In the study of groups and topological spaces, the properties of both are often encountered in one system. The following are common examples: groups with discrete topologies, the complex numbers with the usual topology, and matrix groups with metric topologies. The need for a study of how algebraic properties and topological properties affect one another when united and interrelated in one system soon becomes evident. Thus the purpose of this thesis is to study the interrelated group and topolo… more
Date: December 1972
Creator: Haffner, Ophelia Darleen
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Topological Groups

Description: 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… more
Date: May 1960
Creator: Carry, Laroy Ray
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Topological Properties of Chains

Description: The purpose of this paper is to define and investigate some of the properties of chains. Particular attention is given to a natural topology for chains, called the interval topology, and how the chain properties and topological properties of chains affect each other.
Date: January 1966
Creator: Womack, Robert A.
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