Date of Award
Spring 1997
Project Type
Dissertation
Program or Major
Mathematics
Degree Name
Doctor of Philosophy
First Advisor
Samuel Shore
Abstract
Neighborhoods have played a fundamental role in general topology since the birth of the field. This work outlines the historial evolution of the notion of neighborhood and employs neighborhood assignments, weak neighborhood assignments, and a naturally induced notion of duality in a study of non-Hausdorff topological spaces. Neighborhood characterizations of various classes of spaces, among them the developable and the pseudometrizable spaces, are obtained. A generalization of topological spaces based upon a primitive notion of neighborhood is explored and examples are supplied to motivate the investigation.
Recommended Citation
Cullinane, Michael Joseph, "Contributions to the theory of neighborhoods and its applications" (1997). Doctoral Dissertations. 1942.
https://scholars.unh.edu/dissertation/1942