Examples and theorems for generalized paracompact topological spaces
Fast, Stephen Hardin
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In this thesis we ansWer a number of unsolved problems in generalized paracompact topological spaces. Examples satisfying the Î¤₄ separation axiom are constructed showing the relationship between the properties B(D,Ï o)-refinability, B( D,Î») -refinability, and weak Î¸-refinability. The properties B(D,Î»)-refinability and weak Î¸-refinability are shown to be strictly weaker than B(D,Ï o)-refinability. Sum theorems, mapping theorems, and Î´-product theorems are obtained for B(D,Ï o)-refinability, weak Î¸-refinability, and several other properties. The Î´-product theorem for B(D,Ï o)-refinability, weak Î´-refinability, and other properties are shown to follow from a new special B(D,Ï o) sum theorem.
- Doctoral Dissertations