Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 42).

Thesis (M. Sc.)--University of Hong Kong, 1999. / Includes bibliographical references.

Thesis (M.U.D.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 89-90) Also available in print.

This paper examines several questions regarding Banach spaces, completeness and compactness of Banach spaces, dual spaces and weak and weak* topologies. Examples of completeness and isometries are given using the c₀ and 𝓁ᴰ spaces. The Hahn-Banach extension theorem is presented, along with some applications. General theory about finite and infinite dimensional normed linear spaces is the bulk of the second chapter. A proof of the uniform boundedness principle is also given. Chapter three talks in detail about dual spaces and weak and weak* topologies. An embedding proof and proofs involving weak and weak compactness are also given. The Cauchy-Bunyakowski-Schwarz inequality and Alaoglu's theorem are also proven.

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This thesis deals with the existence and properties of certain types of covering spaces. It contains the discussion of a generalization of the notion of simple connectedness and several well-known theorems depending on this. / Thesis / Master of Science (MS)

This paper investigates the compact-open topology on the set of C_k(X) of continuous real-valued functions defined on a Tychonoff space X. More precisely, we study the following problem: If P is a topological property, does there exist a topological property Q so that C_k(X) has P if and only if X has Q? Characterizations of many properties are obtained throughout the thesis, sometimes modulo some “mild” restrictions on the space X. The main properties involved are summarized in a diagram in the introduction. / Ph. D.

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The goal of this paper is to characterize, at least partially, upper semi-continuous decompositions of topological spaces and the role that upper semi-continuity plays in preserving certain topological properties under decomposition mappings. Attention is also given to establishing what role upper semi-continuity plays in determining conditions under which decomposition spaces possess certain properties. A number of results for non-upper semi-continuous decompositions are included to help clarify the scope of the part upper semi-continuity plays in determining relationships between topological spaces and their decomposition spaces.

We present the results from three papers concerning partitions of vector spaces V over the set R of reals and of the set of lines in V.