UNT Theses and Dissertations - 9 Matching Results

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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
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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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
Item Type: Refine your search to only Thesis or Dissertation
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
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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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.
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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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
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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