منابع مشابه
Space of Valuations
This paper illustrates the general program of applying point-free topology to constructive mathematics, and especially abstract commutative algebra [5, 4, 6, 7, 10, 21], on the notion of valuations. Historically, it can be argued that it is, well before Stone [22], one of the first example of point-free, and algebraic, representation of spaces [3]. The notion of valuation was indeed introduced ...
متن کاملSpace of Valuations
We present a constructive interpretation of some results in [6]. To any integral domain R we associate a distributive lattice V (R) which is a point-free presentation of the space of valuations over the ring R. Our definition, by generators and relations, is similar to Joyal’s definition of the Zariski lattice of a ring R, which is a point-free presentation of the Zariski spectrum of R. The spa...
متن کاملSpace of Valuations
The general framework of this paper is a reformulation of Hilbert’s program using the theory of locales, also known as formal or point-free topology [28, 12, 33]. Formal topology presents a topological space, not as a set of points, but as a logical theory which describes the lattice of open sets. Points are then infinite ideal objects, defined as particular filters of neighborhoods, while basi...
متن کاملThe Space of Isometry Covariant Tensor Valuations
It is known that the basic tensor valuations which, by a result of S. Alesker, span the vector space of tensor-valued, continuous, isometry covariant valuations on convex bodies, are not linearly independent. P. McMullen has discovered linear dependences between these basic valuations and has implicitly raised the question as to whether these are essentially the only ones. The present paper pro...
متن کاملIsometry-Invariant Valuations on Hyperbolic Space
Hyperbolic area is characterized as the unique continuous isometry invariant simple valuation on convex polygons in H. We then show that continuous isometry invariant simple valuations on polytopes in H for n ≥ 1 are determined uniquely by their values at ideal simplices. The proofs exploit a connection between valuation theory in hyperbolic space and an analogous theory on the Euclidean sphere...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2009
ISSN: 0168-0072
DOI: 10.1016/j.apal.2008.09.003