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in creator/contributor: "Sari, Bunyamin"

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Urysohn ultrametric spaces and isometry groups.

In this dissertation we study a special sub-collection of Polish metric spaces: complete separable ultrametric spaces. Polish metric spaces have been studied for quite a long while, and a lot of results have been obtained. Motivated by some of earlier research, we work on the following two main parts in this dissertation. In the first part, we show the existence of Urysohn Polish R-ultrametric spaces, for an arbitrary countable set R of non-negative numbers, including 0. Then we give point-by-p… more

Date: May 2009

Creator: Shao, Chuang

Item Type: Thesis or Dissertation

Partner: UNT Libraries

open access

A Classification of the Homogeneity of Countable Products of Subsets of Real Numbers

Spaces such as the closed interval [0, 1] do not have the property of being homogeneous, strongly locally homogeneous (SLH) or countable dense homogeneous (CDH), but the Hilbert cube has all three properties. We investigate subsets X of real numbers to determine when their countable product is homogeneous, SLH, or CDH. We give necessary and sufficient conditions for the product to be homogeneous. We also prove that the product is SLH if and only if X is zero-dimensional or an interval. And f… more

Date: August 2017

Creator: Allen, Cristian Gerardo

Item Type: Thesis or Dissertation

Partner: UNT Libraries

open access

Trees and Ordinal Indices in C(K) Spaces for K Countable Compact

In the dissertation we study the C(K) spaces focusing on the case when K is countable compact and more specifically, the structure of C() spaces for < ω1 via special type of trees that they contain. The dissertation is composed of three major sections. In the first section we give a detailed proof of the theorem of Bessaga and Pelczynski on the isomorphic classification of C() spaces. In due time, we describe the standard bases for C(ω) and prove that the bases are monotone. In the second s… more

Date: August 2015

Creator: Dahal, Koshal Raj

Item Type: Thesis or Dissertation

Partner: UNT Libraries

open access

Infinitary Combinatorics and the Spreading Models of Banach Spaces

Spreading models have become fundamental to the study of asymptotic geometry in Banach spaces. The existence of spreading models in every Banach space, and the so-called good sequences which generate them, was one of the first applications of Ramsey theory in Banach space theory. We use Ramsey theory and other techniques from infinitary combinatorics to examine some old and new questions concerning spreading models and good sequences. First, we consider the lp spreading model problem which asks… more

Date: May 2019

Creator: Krause, Cory A.

Item Type: Thesis or Dissertation

Partner: UNT Libraries

open access

On the density of minimal free subflows of general symbolic flows.

This paper studies symbolic dynamical systems {0, 1}G, where G is a countably infinite group, {0, 1}G has the product topology, and G acts on {0, 1}G by shifts. It is proven that for every countably infinite group G the union of the minimal free subflows of {0, 1}G is dense. In fact, a stronger result is obtained which states that if G is a countably infinite group and U is an open subset of {0, 1}G, then there is a collection of size continuum consisting of pairwise disjoint minimal free subfl… more

Date: August 2009

Creator: Seward, Brandon Michael

Item Type: Thesis or Dissertation

Partner: UNT Libraries

open access

On Steinhaus Sets, Orbit Trees and Universal Properties of Various Subgroups in the Permutation Group of Natural Numbers

In the first chapter, we define Steinhaus set as a set that meets every isometric copy of another set at exactly one point. We show that there is no Steinhaus set for any four-point subset in a plane.In the second chapter, we define the orbit tree of a permutation group of natural numbers, and further introduce compressed orbit trees. We show that any rooted finite tree can be realized as a compressed orbit tree of some permutation group. In the third chapter, we investigate certain classes of … more

Date: August 2012

Creator: Xuan, Mingzhi

Item Type: Thesis or Dissertation

Partner: UNT Libraries

open access

On the Subspace Dichotomy of Lp[0; 1] for 2 < p < ∞

The structure and geometry of subspaces of a given Banach space is among the most fundamental questions in Functional Analysis. In 1961, Kadec and Pelczyński pioneered a field of study by analyzing the structures of subspaces and basic sequences in L_p[0,1] under a naturally occurring restriction of p, 2 < p <\infty. They proved that any infinite-dimensional subspace X\subset L_p[0,1] for 2<p<\infty must either be isomorphic to l_2 and complemented in L_p or must contain a complemented subspace… more

Date: August 2021

Creator: James, Christopher W

Item Type: Thesis or Dissertation

Partner: UNT Libraries

open access

Duals of Tirilman spaces have unique subsymmetric basic sequences

Article describes how the Tirilman spaces were introduced by Casazza and Shura as variations of the spaces constructed by Tzafriri. We prove that all subsymmetric basic sequences in the dual space are equivalent to its canonical subsymmetic but not symmetric basis.

Date: September 5, 2023

Creator: Dilworth, Steven J.; Kutzarova, Denka; Sari, Bünyamin & Stankov, Svetozar

Item Type: Article

Partner: UNT College of Science

open access

Algebraically Determined Semidirect Products

Let G be a Polish group. We say that G is an algebraically determined Polish group if given any Polish group L and any algebraic isomorphism from L to G, then the algebraic isomorphism is a topological isomorphism. We will prove a general theorem that gives useful sufficient conditions for a semidirect product of two Polish groups to be algebraically determined. This will smooth the way for the proofs for some special groups. For example, let H be a separable Hilbert space and let G be a subset… more

Date: May 2011

Creator: Jasim, We'am Muhammad

Item Type: Thesis or Dissertation

Partner: UNT Libraries