Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002. / Includes bibliographical references (leaves 22). Also available in electronic version. Access restricted to campus users.

We are going to study the remote points in βR and the P-points in βR - R. A remote point in βR is a point which is not in the βR chosure of any discrete subset of R. A point p ε βR - R is a P-point of βR - R if every Gδ-set containing p is a neighbourhood of p. / Science, Faculty of / Mathematics, Department of / Graduate

Thesis (Ph.D.)--Bowling Green State University, 2009. / Document formatted into pages; contains vi, 119 p. Includes bibliographical references.

Thesis (Ph.D.)--University of Central Florida, 2008. / Adviser: Ram N. Mohapatra. Includes bibliographical references (p. 74-76).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin, 1965. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

No description available.

We study the relations between algebraic properties of certain rings of functions and topological properties of the spaces on which the functions are defined. We begin by considering the relation between ideals of rings of functions and z-filters. Let [fomula omitted] be the ring of all m-times differentiable functions on a [formula omitted] differentiable n-manifold X , [formula omitted] the ring of all Lc-functions on a metric space X , and [formula omitted] the ring of all analytic functions on a subset X of the complex plane. It is proved that two m-(resp. Lc-) realcompact spaces X and Y are [formula omitted] diffeomorphic (resp. Lc-homeomorphic) iff [formula omitted] are ring isomorphic. Again if X and Y are m-(resp. Lc-) realcompact spaces, then X can be [formula omitted] (resp.Lc-) embedded as an open [resp. closed] subset in Y iff [formula omitted] homomorphic image of [formula omitted]. The subrings of [formula omitted] which determine the [formula omitted] diffeomorphism (resp. Lc-homeomorphism) of the spaces are studied. We also establish a representation for a transformation, more general than homomorphism, from a ring of [formula omitted] differentiable functions to another ring of [formula omitted] differentiable functions. Finally, we show that, for arbitrary subsets X and Y of the complex plane, if there is a ring isomorphism from [formula omitted] which is the identity on the constant functions, then X and Y are conformally equivalent. / Science, Faculty of / Mathematics, Department of / Graduate

Thesis--Göttingen.