Virginia Polytechnic Institute and State University
The property B(P,[alpha])-refinability and its relationship to generalized paracompact topological spaces
Abstract
dc:description.abstractThe property B(P,∝)-refinability is studied and is used to obtain new covering characterizations of paracompactness, collectionwise normality, subparacompactness, d-paracompactness, a-normality, mesocompactness, and related concepts. These new characterizations both generalize and unify many well-known results. The property B(P,∝)-refinability is strictly weaker than the property Θ-refinability. A B(P,∝)-refinement is a generalization of a σ-locally finite-closed refinement. Here ∝ is a fixed ordinal which dictates the number of "levels" in a given refinement, and P represents a property such as discreteness or local finiteness which each "level" must satisfy relative to a certain subspace.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Polytechnic Institute and State University
- Year dc:date.issued
- 1987
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Price, Ray Hampton
- Chair dc:contributor.committeechair
-
- Smith, James C.
- Committee members dc:contributor.committeemember
-
- Green, E.L.
- McCoy, Robert A.
- Hagedorn, George
- Arnold, Jesse T.
Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Handle dc:identifier.uri
- http://hdl.handle.net/10919/49871
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/49871