{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/49871"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/49871","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"The property B(P,[alpha])-refinability and its relationship to generalized paracompact topological spaces","abstract":"The 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.","abstract_html":"The 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.","abstract_has_math":false,"creators":["Price, Ray Hampton"],"institution":"Virginia Polytechnic Institute and State University","degree_name":"Ph. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. 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