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Thesis (Ph.D.)--Tufts University, 2001. / Adviser: Alva Couch. Submitted to the Dept. of Computer Science. Includes bibliographical references (leaves 144-148). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

We present data structures and algorithms for sets and some generalizations thereof (fuzzy sets, multisets, and fuzzy multisets) available for R through the sets package. Fuzzy (multi-)sets are based on dynamically bound fuzzy logic families. Further extensions include user-definable iterators and matching functions. (authors' abstract)

The purpose of this paper is to examine selected topologies, the Vietoris topology in particular, on S(X), the collection of nonempty, closed subsets of a topological space X. Characteristics of open and closed subsets of S(X), with the Vietoris topology, are noted. The relationships between the space X and the space S(X), with the Vietoris topology, concerning the properties of countability, compactness, and connectedness and the separation properties are investigated. Additional topologies are defined on S(X), and each is compared to the Vietoris topology on S(X). Finally, topological convergence of nets of subsets of X is considered. It is found that topological convergence induces a topology on S(X), and that this topology is the Vietoris topology on S(X) when X is a compact, Hausdorff space.

Let M be the class of simple matroids which do not contain the 5-point line U2,5 , the Fano plane F7 , the non-Fano plane F7- , or the matroid P7 , as minors. Let h(n) be the maximum number of points in a rank-n matroid in M. We show that h(2)=4, h(3)=7, and h(n)=n(n+1)/2 for n>3, and we also find all the maximum-sized matroids for each rank.

In this paper we examine continuous functions which on the surface seem to defy well-known mathematical principles. Before describing these functions, we introduce the Baire Category theorem and the Cantor set, which are critical in describing some of the functions and counterexamples. We then describe generic continuous functions, which are nowhere differentiable and monotone on no interval, and we include an example of such a function. We then construct a more conceptually challenging function, one which is everywhere differentiable but monotone on no interval. We also examine the Cantor function, a nonconstant continuous function with a zero derivative almost everywhere. The final section deals with products of derivatives.

Akademisk afhandling (doktorsvärdighet) -- Uppsala. / Bibliography: p. [v]

Thesis (Ph. D.)--University of Wisconsin--Madison, 1971. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 54-55).

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.

This paper was written in response to the following question: what conditions are sufficient to guarantee that if a compact subset A of a topological linear space L^3 is not convex, then for every point x belonging to the complement of A relative to the convex hull of A there exists a line segment yz such that x belongs to yz and y belongs to A and z belongs to A? Restated in the terminology of this paper the question bay be given as follow: what conditions may be imposed upon a compact subset A of L^3 to insure that A is braced?