Title page for ETD etd-02012006-141709

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
  • Topological spaces research
Date of Defense 1990-12-05
Availability restricted

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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