A construction is given for which the Hausdorff measure and dimension of an arbitrary abstract compact metric space (X, d) can be encoded in a spectral triple. By introducing the concept of resolving sequence of open covers, conditions are given under which the topology, metric, and Hausdorff measure can be recovered from a spectral triple dependent on such a sequence. The construction holds for arbitrary compact metric spaces, generalizing previous results for fractals, as well as the original setting of manifolds, and also holds when Hausdorff and box dimensions differ---in particular, it does not depend on any self-similarity or regularity conditions on the space. The only restriction on the space is that it have positive s₀ dimensional Hausdorff measure, where s₀ is the Hausdorff dimension of the space, assumed to be finite. Also, X does not need to be embedded in another space, such as Rⁿ.

Thesis (M. Arch.)--University of Hong Kong, 2001. / Includes bibliographical references.

Thesis (M. Arch.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 55-56).

Thesis (M. Arch.)--University of Hong Kong, 1999. / Includes special study report entitled: Transitional spaces : a study of figure-ground relationship. Includes bibliographical references.

Thesis (M. Arch.)--University of Hong Kong, 2000. / Includes special study report entitled: From situationist to Hong Kong urbanism. Includes bibliographical references.

Thesis (M. Arch.)--University of Hong Kong, 2002. / Includes special study report entitled: Study of foothill neigborhoods south of Queen's road. Includes bibliographical references.

Thesis (M. Arch.)--University of Hong Kong, 1994. / Includes special report study entitled: Clarity in urban/architectural morphology. Includes bibliographical references.

Thesis (M. Arch.)--University of Hong Kong, 2000. / Includes special report study entitled: Perception of space in motion. Includes bibliographical references.

Thesis (Ph. D.)--York University, 2001. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 86-87). Also available on the Internet. MODE OF ACCESS via web browser by e506ring the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ66351.

We study analogues, in the Lipschitz and Operator Spaces categories, of several classical ideals of operators between Banach spaces. We introduce the concept of a Banach-space-valued molecule, which is used to develop a duality theory for several nonlinear ideals of operators including the ideal of Lipschitz p-summing operators and the ideal of factorization through a subset of a Hilbert space. We prove metric characterizations of p-convex operators, and also of those with Rademacher type and cotype. Lipschitz versions of p-convex and p-concave operators are also considered. We introduce the ideal of Lipschitz (q,p)-mixing operators, of which we prove several characterizations and give applications. Finally the ideal of completely (q,p)-mixing maps between operator spaces is studied, and several characterizations are given. They are used to prove an operator space version of Pietsch's composition theorem for p-summing operators.