Type of Document Dissertation Author Fast, Stephen Hardin URN etd-02012006-141709 Title Examples and theorems for generalized paracompact topological spaces Degree PhD Department Mathematics Advisory Committee
Advisor Name Title Smith, James C. Committee Chair Fletcher, Peter Committee Member Green, Edward L. Committee Member McCoy, Robert A. Committee Member Parry, Charles J. Committee Member Keywords
- Topological spaces research
Date of Defense 1990-12-05 Availability restricted Abstract
In this thesis we ansWer a number of unsolved problems in generalized paracompact topological spaces. Examples satisfying the Τ4 separation axiom are constructed showing the relationship between the properties B(D,ωo)-refinability, B( D,λ) -refinability, and weak θ-refinability. The properties B(D,λ)-refinability and weak θ-refinability are shown to be strictly weaker than B(D,ωo)-refinability.
Sum theorems, mapping theorems, and δ-product theorems are obtained for B(D,ωo)-refinability, weak θ-refinability, and several other properties. The δ-product theorem for B(D,ωo)-refinability, weak δ-refinability, and other properties are shown to follow from a new special B(D,ωo) sum theorem.
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