Surgery and Geometric Topology : Proceedings of the conference held at Josai University 17-20 September, 1996

Ideas from the theory of topological stability of smooth maps are transportedinto the controlled topological category. For example, the controlled topologicalequivalence of maps is discussed. These notions are related to the classi cation ofmanifold approximate brations and manifold strati ed approximate brations. Inturn, these maps form a bundle theory which can be used to describe neighborhoodsof strata in topologically strati ed spaces.Surgery and Geometric Topology : Proceedings of the conference held at Josai University 17-20 September, 1996 / edited by Andrew Ranicki and Masayuki Yamasaki. 本文データは許諾を得てeditorのHPサイトhttp://surgery.matrix.jp/math/josai96/proceedings.html から複製再利用したものである

Bounded distortion homeomorphisms on ultrametric spaces

It is well-known that quasi-isometries between R-trees induce power quasi-symmetric homeomorphisms between their ultrametric end spaces. This paper investigates power quasi-symmetric homeomorphisms between bounded, complete, uniformly perfect, ultrametric spaces (i.e., those ultrametric spaces arising up to similarity as the end spaces of bushy trees). A bounded distortion property is found that characterizes power quasi-symmetric homeomorphisms between such ultrametric spaces that are also pseudo-doubling. Moreover, examples are given showing the extent to which the power quasi-symmetry of homeomorphisms is not captured by the quasiconformal and bi-H\"older conditions for this class of ultrametric spaces.Comment: 20 pages, 1 figure. To appear in Ann. Acad. Sci. Fenn. Mat

DOI: 10.1017/S0017089503001496. Printed in the United Kingdom NEIGHBORHOODS OF STRATA IN MANIFOLD STRATIFIED SPACES

Abstract. Strata in manifold stratified spaces are shown to have neighborhoods that are teardrops of manifold stratified approximate fibrations (under dimension and compactness assumptions). This is the best possible version of the tubular neighborhood theorem for strata in the topological setting. Applications are given to replacement of singularities, to the structure of neighborhoods of points in manifold stratified spaces, and to spaces of manifold stratified approximate fibrations

Textual and hermeneutical aspects of Paul's use of the Old Testament in 1 and 2 Corinthians

Part I presents the textual and conceptual vectors which form the background to the specific examination of the OT in 1 and 2 Cor. Ihe first aim is to discern the original OT text-forms in order to conclude what was or was not a Pauline alteration. Septuagintal transmission-history in first century Palestine is discussed in the light of recent methodological advances made by Barthelemy, Cross and others. The paper follows, in the main, the established positions of Barthelemy and Tov. The second aim concerns why Paul selected and, in several cases, edited the OT texts. Oral and written tradition in Palestine is examined by interaction with the critical debates centered on the works of Gerhardsson and others. Distinctions between literary form and exegetical method are made in view of possible anachronistic errors when comparing early Christianity with Judaism and Rabbinics. Part I concludes by surveying nine major works specifically concerning Paul's use of the OT. A caveat arises to consider Paul's own usage apart from the imposition of a later critical method.Part II contains the detailed observation of the textual and hermeneutical evidences. Organized by OT books, each passage is examined on textual, contextual and hermeneutical levels. A cumulative perspective of Paul's textual bases and hermeneutical methods and conceptualities emergesPart III presents the textual and conceptual con¬ clusions. Hermeneutically, Paul shows a consistent tendency to use the OT for more than anti-Judaistic polemic (Lindars) or simple illustration (Ulonska). The basis of his use was an historical understanding of the OT. Paul's conceptuality displays a continuity of deity and piety from the OT to the NT. The conclusions of Harnack, Dodd, Lindars, Braun and others concerning Paul's concepts of continuity are evaluated in this light. The paper concludes with an elaboration of possible in¬ dications of a Palestinian Greek OT in 1 and 2 Cor. Textually, Paul shows positive evidence for a Palestin¬ ian Greek OT divergent from the LXX. In the absence of evidence from Qumran, Paul's OT text-forms provide early evidence for the state of the Greek OT in Palestin