Settings and notions are as in previous abstracts of W. D. L. Appling. This paper contains an investigation of the relationship between a class of non-linear functions defined on PAB and certain subspaces of PAB in particular Appling's linear C-sets, Solomon leader's finitely additive Lp spaces, and one of the projective limit spaces studied by Davis, Murray, and Weber.

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For the case where L is an ecl-premonoid, we explore various characterizations of SL-topological spaces, in particular characterization in terms of a convergence function lim: FS L(X) ! LX. We find we have to introduce a new axiom , L on the lim function in order to completely describe SL-topological spaces, which is not required in the case where L is a frame. We generalize the classical Kowalski and Fischer axioms to the lattice context and examine their relationship to the convergence axioms. We define the category of stratified L-generalized convergence spaces, as a generalization of the classical convergence spaces and investigate conditions under which it contains the category of stratified L-topological spaces as a reflective subcategory. We investigate some subcategories of the category of stratified L-generalized convergence spaces obtained by generalizing various classical convergence axioms.

The aim of this thesis is to prove the existence of the Shilov boundary and the minimal boundary with respect to some function algebras and investigate their topological structures. / Science, Faculty of / Mathematics, Department of / Graduate

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1981 / Bibliography: leaves 102-103. / by Javier Bracho. / Ph. D. / Ph.D. Massachusetts Institute of Technology, Department of Mathematics

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This thesis deals with the relationships between covering properties and properties of compatible quasi-uniformities of a topological space. The covering properties considered in this work are orthocompactness, metacompactness and paracompactness; some generalizations of orthocompactness are also defined and studied. / Ph. D.

In this thesis we answer a number of unsolved problems in generalized paracompact topological spaces. Examples satisfying the T₄ separation axiom are constructed showing the relationship between the properties B(D, ω₀)-refinability, B(D, λ)-refinability, and weak θ̅-refinability. The properties B(D, λ)-refinability and weak θ̅-refinability are shown to be strictly weaker than B(D, ω₀)-refinability. Sum theorems, mapping theorems, and o—product theorems are obtained for B(D, ω₀)-refinability, weak θ̅-refinability, and several other properties. The σ—product theorem for B(D,ω₀)-refinability, weak θ̅-refinability, and other properties are shown to follow from a new special B(D,ω₀) sum theorem. / Ph. D.

This thesis is an investigation of the concept of paracompactness. It presents the history of paracompactness, analyzes this concept from several diverse points of view and tries to establish the relationship between these different views. The starting point is the work of Tukey [40]. The important problem of the metrization of topological spaces is presented as an application of the concept of paracompactness. / Master of Science