acase@tulane.edu

In this thesis we investigate contractibility and local contractibility in the hyperspace of subcontinua of continuum X. We show that C(X) is contractible if and only if it is freely contractible to the point X. Since free contractibility to a point in a continuum is equivalent to arc-smoothness at that point, this shows that C(X) is arc-smooth at the point X for any continuum X such that C(X) is contractible, answering a question of Goodykoontz We also show that if C(X) is contractible and (mu)('-1)(t(,0)) is irreducible between two points for some t(,0), then there is a map from C(X) onto (mu)('-1)(t(,0)). Furthermore, this map remains surjective when restricted to a separating subcontinuum of C(X). In certain cases, these theorems imply that C(X) cannot be embedded in E('3) We give conditions which imply the local contractibility of C(X). These conditions are very weak in the sense that it is not known whether or not there is a continuum for which they are not satisfied. It remains an open question whether or not C(X) is always locally contractible at the point X Duda has given a geometric construction for the hyperspace of subcontinua of a finite acyclic graph. We construct the hyperspace of a bouquet of circles by expressing it as a quotient space of the hyperspace of an acyclic graph. This construction is used to show that the property of being an ANR is not strongly Whitney reversible. Also, we are able to construct, as a quotient space of the hyperspace of an acyclic graph, the hyperspace of any finite graph. These results answer questions of Duda {3} and Nadler {13} / acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

In this thesis we investigate the existence of superdecomposable modules over integral domains, i.e. of modules which do not have any non-zero indecomposable direct summands. We generalize a result of Benabdallah and Birtz {1} about superdecomposable abelian groups and present constructions of superdecomposable modules over noetherian domains, generalized Krull domains, certain valuation domains, and h-local domains. We classify the Dedekind domains and Krull domains of characteristic zero which admit superdecomposable modules / acase@tulane.edu

The purpose of this dissertation is to show that an inherently moral use of reason, which according to Kant presupposes the existence of an eternal intelligible order, is possible precisely due to the design of the self's temporality. I develop an account of temporality which is guided by Heidegger's attempt in Being and Time to define the conditions which are necessary for the individual to choose himself in light of his finitude. On that basis, I outline the design of a normative ethic which is consistent with Kant's Foundation for the Metaphysics of Morals. By developing Heidegger's explanation of the individualizing function inherent in each of us (i.e., the call of conscience), I show that Being and Time is a continuation of the task which Kant himself initiated in the Foundation for the Metaphysics of Morals In the course of this essay, I employ Heidegger's threefold phenomenological method of construction, reduction, and destruction to remove Kant's ethics from its artificial architectonic and to retrieve its essential elements within an existential framework. Ultimately, I establish that the freedom to follow unconditioned moral commands arises precisely from the individual's ability to affirm the limitations inherent in his existence. This analysis constitutes an existential formulation of the Kantian thesis 'ought implies can.' I conclude that the faculty Kant himself identified for applying a rule in a specific case, namely, the transcendental imagination, is the basis for moral judgments. This conclusion substantiates Heidegger's central thesis in Kant and the Problem of Metaphysics that the imagination is the root of human reason in both its theoretical and practical employment / acase@tulane.edu

acase@tulane.edu

acase@tulane.edu