Thesis (Ph. D.)--Oregon State University, 1996. / Typescript (photocopy). Includes bibliographical references (leaves 68-69). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1973. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

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 clarify the scope of the part upper semi-continuity plays in determining relationships between topological spaces and their decomposition spaces.

The purpose of this paper is to examine selected topologies, the Vietoris topology in particular, on S(X), the collection of nonempty, closed subsets of a topological space X. Characteristics of open and closed subsets of S(X), with the Vietoris topology, are noted. The relationships between the space X and the space S(X), with the Vietoris topology, concerning the properties of countability, compactness, and connectedness and the separation properties are investigated. Additional topologies are defined on S(X), and each is compared to the Vietoris topology on S(X). Finally, topological convergence of nets of subsets of X is considered. It is found that topological convergence induces a topology on S(X), and that this topology is the Vietoris topology on S(X) when X is a compact, Hausdorff space.

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 by specially defined order related properties called order-convergence and star-convergence.

Thesis (Ph. D.)--School of Industrial and Systems Engineering, Georgia Institute of Technology, 2004. Directed by George L. Nemhauser. / Vita. Includes bibliographical references (leaves 91-94).

Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2005. / Includes bibliographical references (leaf 15).

This paper contains a discussion of topological dimension theory. Original proofs of theorems, as well as a presentation of theorems and proofs selected from Ryszard Engelking's Dimension Theory are contained within the body of this endeavor. Preliminary notation is introduced in Chapter I. Chapter II consists of the definition of and theorems relating to the small inductive dimension function Ind. Large inductive dimension is investigated in Chapter III. Chapter IV comprises the definition of covering dimension and theorems discussing the equivalence of the different dimension functions in certain topological settings. Arguments pertaining to the dimension o f Jn are also contained in Chapter IV.

Thesis (Ph.D.)--McMaster University, 2003. / Advisor: Ian Hambleton. Includes bibliographical references (leaves 109-112). Also available via World Wide Web.