Thesis (M.C.S.) Carleton University, 2005. / Includes bibliographical references (p. 36-41). Also available in electronic format on the Internet.

Habilitationsschrift--Bonn. / Bibliography: p. 81.

Thesis (Ph. D.)--University of North Texas, May, 2009. / Title from title page display. Includes bibliographical references.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2004. / Includes bibliographical references (p. 99-102).

No description available.

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.

No description available.

This thesis verified that metric spaces can be constructed using ultrametrics d and D, where d(x,y) = 0 if x = y and d(x,y) = (1/2) k if x not equal to y, such that x-y = 2k(a/b) for a,b relatively prime to 2, and where D(A,B)= max(d(al,bl); d(a2,b2)) for A = (al,a2) and B = (bl,b2).Assuming that a line is represented by some linear equation, a one-dimensional point was defined as an element of Q and a two-dimensional point as an element of Q x Q. There was an investigation of one-dimensional points with respect to the behavior of segments, midpoints, and distances as measured by d. The function D demonstrated the behavior of midpoints, medians, and triangles, as well as the congruence relation. The study necessitated the introduction of pseudomidpoints and pseudomedians, and an unorthodox definition of angle measurement.

Thesis (Ph. D. in Mathematics)--Vanderbilt University, May 2008. / Title from title screen. Includes bibliographical references.

Thesis (Ph. D.)--Rutgers University, 2007. / "Graduate Program in Mathematics." Includes bibliographical references (p. 82-85).