Thesis (Ph. D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1998. / Includes bibliographical references (p. 117-121).

Thesis (M.S.)--Tennessee Technological University, 2008. / Title from title page screen (viewed on Sept. 29, 2009). Bibliography: leaves 32-33.

Proefschrift--Amsterdam, 1931.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1976. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Inaug.-diss.--Münster.

A topological space may be viewed as an algebraic structure. For example, it may be viewed as a (complete atomic) Boolean algebra equipped with a closure operator. The lattice of closed subsets is another algebraic structure which may be associated with a topological space. Tne purpose of this thesis is primarily to investigate the metamathematical properties of algebraic structures associated with topological spaces. More specifically, we will first consider questions of decidability of the theories of these algebraic structures. It turns out that these theories are undecidable. We will also examine certain equivalence relations on the class of topological spaces that arise naturally from viewing them as first-order structures. Finally we will show that certain classical theorems of model theory do not hold for topological spaces. / Science, Faculty of / Mathematics, Department of / Graduate

This thesis explores some results of two topological spaces.

The purpose of this paper is to further investigate R0 spaces, R1 spaces, and hyperspaces. The R0 axiom was introduced by N. A. Shanin in 1943. Later, in 1961, A. S. Davis investigated R0 spaces and introduced R1 spaces. Then, in 1975, William Dunham further investigated R1 spaces and proved that several well-known theorems can be generalized from a T2 setting to an R1 setting. In Chapter II R0 and R1 spaces are investigated and additional theorems that can be generalized from a T2 setting to an R1 setting are obtained.

Band structures of ultrathin films of heavy elements, £\-Sn and Sb, were investigated using first-principle calculations with the inclusion of spin-orbit coupling. The band structures were gradually varied as the physical parameters were adjusted. The band inversion was obtained at the high symmetry point in Brillouin zone, making a topological phase transition. In this study, the band inversion at £F point of the Brillouin zone was predicted in single bi-layer of Sb(111) and single bi-layer and two bi-layers of £\-Sn(111). The topological phase transition is from trivial insulator to topological insulator for single bi-layer of Sb(111). Finally, the topological phase transition is from trivial semi-metal to topological semi-metal for single bi-layer of £\-Sn(111), whereas as it is from topological semi-metal to trivial metal for two bi-layers of £\-Sn(111).

Thesis (Ph.D.)--Baylor University, 2009. / Includes bibliographical references (p. 66-68).