Examples and theorems for generalized paracompact topological spaces

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,Ï _o)-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,Ï _o)-refinability.

Sum theorems, mapping theorems, and δ-product theorems are obtained for B(D,Ï _o)-refinability, weak θ-refinability, and several other properties. The δ-product theorem for B(D,Ï _o)-refinability, weak δ-refinability, and other properties are shown to follow from a new special B(D,Ï _o) sum theorem.