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Untersuchungen über Unabhängigkeit und Tragweite der Axiome der Mengenlehre in der Axiomatik Zermelos und FraenkelsVieler, Heinrich, January 1926 (has links)
Inaug.Diss.Marburg. / Vita. Bibliography: 5th prelim. p.

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Mengen und Mächtigkeiten eine erkenntniskritische Studie /Sganzini, Carlo. January 1913 (has links)
Inaug.diss.Universität Bern. / "Literatur": p. [137]38.

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Abstract resourcebound classesBoas, Peter van Emde. January 1974 (has links)
Academisch proefschrift. / Includes bibliographical references.

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Ensembles ordonnées et ramifiés ...Kurepa, Georges. January 1935 (has links)
ThèseUniv. de Paris.

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On some definitions of a finite setGutteridge, Lance January 1969 (has links)
Six definitions of a finite set are studied; and each implication between the definitions is shown to be either derivable from the ZermeloFraenkel axioms or independent
of them. The method of Booleanvalued models, as studied by D. Scott, is used to show that it is consistent with the ZermeloFraenkel axioms to deny some of these implications by constructing appropriate models.
The six definitions are shown to satisfy a list of properties which a definition of finite should reasonably possess. It is also shown that any definition which satisfies these properties must encompass a larger class of sets than the first definition and a smaller class than the sixth.
Three more definitions, which do not possess these properties, are mentioned, and the differences between these definitions and the first six are discussed. / Science, Faculty of / Mathematics, Department of / Graduate

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Souslin's conjecture and some equivalencesDaniel, Ian Alistair January 1971 (has links)
This thesis deals with some equivalences to Soulin's hypothesis.
Also included is a consequence of its negation, the existence of a normal Hausdorff space which is not countably paracompact. Two equivalences to Souslin's hypothesis can be obtained by considering the countable chain condition in the product with itself of an ordered continuum and by considering Peano maps on ordered continua. An equivalence to a negative answer is the existence of a tree of cardinality, [formula omitted] ₁, in which every chain and
antichain (set of pairwise incomparable objects) is countable. Another equivalence to Souslin's hypothesis is obtained by assuming that a continuum which is the continuous image of an ordered continuum is metrizable if and only if it has the countable chain condition. We get yet another by assuming that a compactum which is the continuous image of an ordered compactum is separable if and only if it has the countable chain condition. Finally, if we restrict ourselves to compacta of the type just mentioned we find that Souslin's hypothesis is equivalent to a generalization of a metrization theorem of S. Mardeśic. / Science, Faculty of / Mathematics, Department of / Graduate

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Complete extensions of ordered setsBallinger, Bruce T. (Bruce Thomas) January 1969 (has links)
No description available.

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Efficient representation of cluster structure in large data sets /Kantabutra, Sanpawat. January 1900 (has links)
Thesis (Ph.D.)Tufts University, 2001. / Adviser: Alva Couch. Submitted to the Dept. of Computer Science. Includes bibliographical references (leaves 144148). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

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Spaces of Closed Subsets of a Topological SpaceLeslie, Patricia J. 08 1900 (has links)
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.

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MaximumSized Matroids with no Minors Isomorphic to U2,5, F7, F7¯, OR P7Mecay, Stefan Terence 05 1900 (has links)
Let M be the class of simple matroids which do not contain the 5point line U2,5 , the Fano plane F7 , the nonFano plane F7 , or the matroid P7 , as minors. Let h(n) be the maximum number of points in a rankn 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 maximumsized matroids for each rank.

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