Dimension Theory
نویسندگان
چکیده
منابع مشابه
Dimension theory and forcing
There is a proper Baire category preserving forcing which adds infinitely equal real but no Cohen real. This resolves a long-standing open problem of David Fremlin. The forcing has a natural description in terms of infinite-dimensional topology.
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In which a theory of dimension related to the Jones index and based on the notion of conjugation is developed. An elementary proof of the additivity and multiplicativity of the dimension is given and there is an associated trace. Applications are given to a class of endomorphisms of factors and to the theory of subfactors. An important role is played by a notion of amenability inspired by the w...
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We show that standard arguments for deformations based on dimension counts can also be applied over a (not necessarily Noetherian) valuation ring A of rank 1. Key intermediate results are a principal ideal theorem for schemes of finite type over A, and a theorem on subadditivity of intersection codimension for schemes smooth over A.
متن کاملLectures on Dimension Theory
Preliminaries In this lecture, we give a quick review of the basics of classical commutative algebra. The following notation and terminology is used throughout. By a ring we mean a commutative ring with identity. For sets I, J, we write I ⊆ J to denote that I is a subset of J and I ⊂ J to denote that I is a proper subset of J, i.e., I ⊆ J and I = J. We denote the set of nonnegative integers by ...
متن کاملDimension Theory Local and Global
These survey lectures are devoted to a new subject of the large scale dimension theory which was initiated by Gromov as a part of asymptotic geometry. We are going to enter the large scale world and consider some new concepts, results and examples which are parallel in many cases to the corresponding elements of the standard (local) dimension theory. We start our presentation with the motivations.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.2307/2038931