A computational model for metric spaces
Abbas Edalat,Reinhold Hackmann +1 more
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TLDR
The computational model BX is used to give domain-theoretic proofs of Banach's fixed point theorem and of two classical results of Hutchinson: on a complete metric space, every hyperbolic iterated function system has a unique non-empty compact attractor, and every iteratedfunction system with probabilities has aunique invariant measure with bounded support.About:
This article is published in Theoretical Computer Science.The article was published on 1998-02-28 and is currently open access. It has received 187 citations till now. The article focuses on the topics: Metric space & Intrinsic metric.read more
Citations
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Journal ArticleDOI
Approximation of Metric Spaces by Partial Metric Spaces
TL;DR: A weak partial metric on the poset of formal balls of a metric space can be used to construct the completion of classical metric spaces from the domain-theoretic rounded ideal completion.
Book ChapterDOI
Nonsymmetric Distances and Their Associated Topologies: About the Origins of Basic Ideas in the Area of Asymmetric Topology
TL;DR: The historic development of what is now often called “Nonsymmetric or Asymmetric Topology” is summarized in Section 2 and in the following, more specific sections the authors discuss thehistoric development of some of the main ideas of the area in greater detail.
Journal ArticleDOI
Domains for computation in mathematics, physics and exact real arithmetic
TL;DR: A survey of the recent applications of continuous domains for providing simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separable metric spaces, separable Banach spaces and spaces of probability distributions is presented.
Journal ArticleDOI
Computability of probability measures and Martin-Löf randomness over metric spaces
Mathieu Hoyrup,Cristobal Rojas +1 more
TL;DR: In this paper, the authors investigated algorithmic randomness on more general spaces than the Cantor space, namely computable metric spaces, and developed a unified framework allowing computations with probability measures.
Journal ArticleDOI
Spaces of maximal points
TL;DR: This paper shows that it is precisely the complete metrizable separable metric spaces that can be realized as the set of maximal points of an ω-continuous dcpo, where the setof maximal points is topologized with the relative Scott topology.
References
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Book
Geometric Measure Theory
TL;DR: In this article, Grassmann algebras of a vectorspace have been studied in the context of the calculus of variations, and a glossary of some standard notations has been provided.
Proceedings Article
Domain theory
Samson Abramsky,Achim Jung +1 more
TL;DR: In this paper, the authors define abstract bases as the bases of compact elements of algebraic domains and define the notion of ideal completion as the relation with which a basis can be equipped.
Proceedings ArticleDOI
A probabilistic powerdomain of evaluations
C. Jones,Gordon Plotkin +1 more
TL;DR: A probabilistic power domain construction is given for the category of inductively complete partial orders and it is the partial order of continuous.
Journal ArticleDOI
Domain theory and integration
TL;DR: A theory of integration based on a new notion of integral which generalises and shares all the basic properties of the Riemann integral is developed, which provides a new technique for computing the Lebesgue integral.