On the Yoneda completion of a quasi-metric space

Künzi, Hans-Peter A.; Schellekens, Michel

doi:10.1016/s0304-3975(00)00335-2

Cited by 58 publications

(48 citation statements)

References 19 publications

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“…In order to help to the reader we recall the construction of the bicompletion of a quasi-metric space (see [2,19] or p. 163 of [13]). pletion of (X, d).…”

Section: From the Above Constructions We Obtainmentioning

confidence: 99%

Weightable quasi-uniformities

Künzi

Romaguera

2012

Acta Math Hung

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Extending the well-known result that every fuzzy metric space, in the sense of Kramosil and Michalek, has a completion which is unique up to isometry, we show that every KM-fuzzy quasi-metric space has a bicompletion which is unique up to isometry, and deduce that for each KM-fuzzy quasi-metric space, the completion of its induced fuzzy metric space coincides with the fuzzy metric space induced by its bicompletion.

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“…In order to help to the reader we recall the construction of the bicompletion of a quasi-metric space (see [2,19] or p. 163 of [13]). pletion of (X, d).…”

Section: From the Above Constructions We Obtainmentioning

confidence: 99%

Weightable quasi-uniformities

Künzi

Romaguera

2012

Acta Math Hung

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“…For instance, balanced 0 quasimetrics induce completely regular Hausdorff topologies (see [1,Corollary 3] and [8,Page 208]) and totally bounded balanced 0 quasimetrics induce uniformities (see [9,10]). Künzi and Kivuvu [11,12] localize Doitchinov's idea of balancedness; that is, they do not work with arbitrary Cauchy filter pairs but only with those that they call balanced Cauchy filter pairs. Before stating the proposed completion theory from Künzi and Kivuvu, we give some definitions from [11].…”

Section: Introductionmentioning

confidence: 99%

A Solution to the Completion Problem for Quasi-Pseudometric Spaces

Andrikopoulos

2013

International Journal of Mathematics and Mathematical Sciences

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The different notions of Cauchy sequence and completeness proposed in the literature for quasi-pseudometric spaces do not provide a satisfactory theory of completeness and completion for all quasi-pseudometric spaces. In this paper, we introduce a notion of completeness which is classical in the sense that it is made up of equivalence classes of Cauchy sequences and constructs a completion for any given 0 quasi-pseudometric space. This new completion theory extends the existing completion theory for metric spaces and satisfies the requirements posed by Doitchinov for a nice theory of completeness.

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“…Hemi-metrics (not taking the value +∞) are called directed metrics by de Alfaro et al [3], and just metrics by Lawvere [18]. While most works on hemi-metrics consist in characterizing notions of limits or completions (see, e.g., [17] and references therein), we shall concentrate on the topology. (In the absence of a definitive textbook on hemi-metrics, we prove these properties in Appendix A.)…”

Section: Preliminariesmentioning

confidence: 99%

“…The topology of X sym is finer (has at least as many opens as) those of X and X op . A hemi-metric space X is totally bounded [17] iff for every > 0, there are finitely many elements x 1 , . .…”

Section: Preliminariesmentioning

confidence: 99%

Simulation Hemi-metrics between Infinite-State Stochastic Games

Goubault-Larrecq

Foundations of Software Science and Computational Structures

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Abstract. We investigate simulation hemi-metrics between certain forms of turnbased 2 1 2 -player games played on infinite topological spaces. They have the desirable property of bounding the difference in payoffs obtained by starting from one state or another. All constructions are described as the special case of a unique one, which we call the Hutchinson hemi-metric on various spaces of continuous previsions. We show a directed form of the Kantorovich-Rubinstein theorem, stating that the Hutchinson hemi-metric on spaces of continuous probability valuations coincides with a notion of trans-shipment hemi-metric. We also identify the class of so-called sym-compact spaces as the right class of topological spaces, where the theory works out as nicely as possible.

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On the Yoneda completion of a quasi-metric space

Cited by 58 publications

References 19 publications

Weightable quasi-uniformities

Weightable quasi-uniformities

A Solution to the Completion Problem for Quasi-Pseudometric Spaces

Simulation Hemi-metrics between Infinite-State Stochastic Games

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