UNT Libraries - 14 Matching Results

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Product and Function Spaces

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.
Date: August 1971
Creator: Barrett, Lewis Elder

On Sets and Functions in a Metric Space

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.
Date: December 1971
Creator: Beeman, Anne L.

Completeness Axioms in an Ordered Field

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.
Date: December 1971
Creator: Carter, Louis Marie

Rings of Continuous Functions

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.
Date: August 1971
Creator: Connell, Carolyn

Radicals of a Ring

Description: The problem with which this investigation is concerned is that of determining the properties of three radicals defined on an arbitrary ring and determining when these radicals coincide. The three radicals discussed are the nil radical, the Jacobsson radical, and the Brown-McCoy radical.
Date: May 1971
Creator: Crawford, Phyllis Jean

Ideals in Quadratic Number Fields

Description: The purpose of this thesis is to investigate the properties of ideals in quadratic number fields, A field F is said to be an algebraic number field if F is a finite extension of R, the field of rational numbers. A field F is said to be a quadratic number field if F is an extension of degree 2 over R. The set 1 of integers of R will be called the rational integers.
Date: May 1971
Creator: Hamilton, James C.

On Lane's Integral

Description: The problem and purpose of this paper is to develop Lane's Integral in two-space, and then to expand these concepts into three-space and n-space. Lane's Integral can be used by both mathematicians and statisticians as one of the tools in the calculation of certain probabilities and expectations. The method of presentation is straightforward with the basic concepts of integration theory and Stieltjes Integral assumed.
Date: August 1971
Creator: Hill, William James

Algebraic Properties of Semigroups

Description: This paper is an algebraic study of selected properties of semigroups. Since a semigroup is a result of weakening the group axioms, all groups are semigroups. One facet of the paper is to demonstrate various semigroup properties that induce the group axioms.
Date: May 1971
Creator: Lumley, Robert Don

Some Properties of Valuation Rings

Description: This thesis investigates some of the properties of valuation rings. It is assumed that the reader is familiar with the basic properties of commutative rings and ideals in rings. Unless otherwise stated, all rings considered in this thesis are commutative rings with a unity.
Date: August 1971
Creator: Miller, Linda C.

Inequalities and Set Function Integrals

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

Uniform Locally Compact Spaces

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.
Date: December 1971
Creator: Page, Perman Hutson

Semitopological Groups

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.
Date: December 1971
Creator: Scroggs, Jack David