Date of Award
Program or Major
Doctor of Philosophy
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.
Cullinane, Michael Joseph, "Contributions to the theory of neighborhoods and its applications" (1997). Doctoral Dissertations. 1942.