Results 231 to 240 of about 3,221 (259)
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On the Upper Completeness of Quasi-metric Spaces
2010 Third International Symposium on Intelligent Information Technology and Security Informatics, 2010This paper is concerned with the problem of upper completeness in the quasi-metric spaces. In this paper, firstly, some new basic concepts of quasi-metric spaces such as the upper limit and lower limit are put forward. Correspondingly, the concepts of upper closed set, upper Cauchy sequence and upper completeness are obtained. Secondly, three important
Xiaodan Chen, Shaobai Chen
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Local Yoneda completions of quasi-metric spaces
Mathematical Structures in Computer Science, 2023AbstractIn this paper, we study quasi-metric spaces using domain theory. Given a quasi-metric space (X,d), we use $({\bf B}(X,d),\leq^{d^{+}}\!)$ to denote the poset of formal balls of the associated quasi-metric space (X,d). We introduce the notion of local Yoneda-complete quasi-metric spaces in terms of domain-theoretic properties of $({\bf B}(X,d)
Jing Lu, Bin Zhao
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Geometry of Quasi-Metric Spaces
2015The main goal of this chapter is to set the stage for the rest of this monograph by presenting a brief survey of some of the many facets of the theory of quasi-metric spaces. Quasi-metric spaces constitute generalizations of not only the classical Euclidean setting, but of quasi-Banach spaces and ultrametric spaces.
Ryan Alvarado, Marius Mitrea
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The space of formal balls and models of quasi-metric spaces
Mathematical Structures in Computer Science, 2009In this paper we study quasi-metric spaces using domain theory. Our main objective in this paper is to study the maximal point space problem for quasi-metric spaces. Here we prove that quasi-metric spaces that satisfy certain completeness properties, such as Yoneda and Smyth completeness, can be modelled by continuous dcpo's.
M. Ali-Akbari +3 more
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The Ultra-Quasi-Metrically Injective Hull of a T 0-Ultra-Quasi-Metric Space
Applied Categorical Structures, 2012This is a technical paper dealing with special classes of spaces and their completions. Let \(X\) be a set and \(u\) be a map of \(X\times X\) into the non-negative reals. Then \(u\) is an ultra-quasi-pseudometric if (i) \(u(x,x) = 0\) for all \(x\in X\) and (ii) \(u(x,z)\leq max\{u(x,y),u(y,z)\}\), whenever \(x,y,z\in X\). If, moreover, \(u(x,y) = 0 =
Hans-Peter A. Künzi +1 more
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A non quasi-metric completion for quasi-metric spaces
1999Within the realm of approach spaces the authors develop, via the use of suitable nearness concepts, a completion theory and apply this to complete quasimetric spaces. In particular, for approach spaces \(X\) they introduce the concepts of near collections, clusters (= maximal near collections) and completeness (i.e., every cluster converges) and ...
Lowen, R., Vaughan, D.
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A characterization of bicompletable fuzzy quasi-metric spaces
Fuzzy Sets and Systems, 2005An internal characterization of fuzzy quasi-metric spaces which admit a fuzzy quasi-metric bicompletion is given, and the uniqueness of such a bicompletion is also proved.
Valentín Gregori +2 more
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Quasi-metric spaces and point-free geometry
Mathematical Structures in Computer Science, 2006An approach to point-free geometry based on the notion of a quasi-metric is proposed in which the primitives are the regions and a non-symmetric distance between regions. The intended models are the bounded regular closed subsets of a metric space together with the Hausdorff excess measure.
DI CONCILIO, Anna, GERLA G. G.
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, 2023 Inspired by the work of Adhya and Ray, I provide my own proof of selected theorems and lemmas discussed in [1]. Original theorems should appear, in due course, in a future article.
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Metrizability of Quasi-Metric Spaces
Journal of the London Mathematical Society, 1977Raghavan, T. G., Reilly, I. L.
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