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Development of a Geometry from a Set of Axioms

Description: The purpose of this paper is to develop a geometry based on fourteen axioms and four undefined terms.
Date: May 1973
Creator: Glasscock, Anita Louise
Partner: UNT Libraries
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Lebesgue-Stieltjes Measure and Integration

Description: The purpose of the thesis is to investigate an approach to Lebesgue-Stieltjes measure and integration.
Date: May 1973
Creator: Seale, Laura S.
Partner: UNT Libraries
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Simplicial Homology

Description: The purpose of this thesis is to construct the homology groups of a complex over an R-module. The thesis begins with hyperplanes in Euclidean n-space. Simplexes and complexes are defined, and orientations are given to each simplex of a complex. The chains of a complex are defined, and each chain is assigned a boundary. The function which assigns to each chain a boundary defines the set of r-dimensional cycles and the set of r—dimensional bounding cycles. The quotient of those two submodules is … more
Date: August 1973
Creator: Chang, Chih-Chen
Partner: UNT Libraries
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Properties of an Integral of E.J. McShane

Description: The problem with which this paper is concerned is that of investigating the properties of an integral which was first defined by E. J. McShane in lecture notes presented at the Conference on Modern Theories of Integration, held at the University of Oklahoma in June, 1969.
Date: August 1973
Creator: Dennis, Thomas B.
Partner: UNT Libraries
open access

Some Properties of Ideals in a Commutative Ring

Description: This thesis exhibits a collection of proofs of theorems on ideals in a commutative ring with and without a unity. Theorems treated involve properties of ideals under certain operations (sum, product, quotient, intersection, and union); properties of homomorphic mappings of ideals; contraction and extension theorems concerning ideals and quotient rings of domains with respect to multiplicative systems; properties of maximal, minimal, prime, semi-prime, and primary ideals; properties of radicals … more
Date: August 1973
Creator: Hicks, Gary B.
Partner: UNT Libraries
open access

R-Modules for the Alexander Cohomology Theory

Description: The Alexander Wallace Spanier cohomology theory associates with an arbitrary topological space an abelian group. In this paper, an arbitrary topological space is associated with an R-module. The construction of the R-module is similar to the Alexander Wallace Spanier construction of the abelian group.
Date: May 1973
Creator: Anderson, Stuart Neal
Partner: UNT Libraries
open access

A Partial Characterization of Upper Semi-Continuous Decompositions

Description: The goal of this paper is to characterize, at least partially, upper semi-continuous decompositions of topological spaces and the role that upper semi-continuity plays in preserving certain topological properties under decomposition mappings. Attention is also given to establishing what role upper semi-continuity plays in determining conditions under which decomposition spaces possess certain properties. A number of results for non-upper semi-continuous decompositions are included to help clari… more
Date: December 1973
Creator: Dennis, William Albert
Partner: UNT Libraries
open access

Topologies on Complete Lattices

Description: One of the more important concepts in mathematics is the concept of order, that is, the description or comparison of two elements of a set in terms of one preceding or being smaller than or equal to the other. If the elements of a set, as pairs, exhibit certain order-type characteristics, the set is said to be a partially ordered set. The purpose of this paper is to investigate a special class of partially ordered sets, called lattices, and to investigate topologies induced on these lattices b… more
Date: December 1973
Creator: Dwyer, William Karl
Partner: UNT Libraries
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