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On the Yoneda completion of a quasi-metric space

H.P. Künzi, M.P. Schellekens
2002 Theoretical Computer Science  
Several theories aimed at reconciling the partial order and the metric space approaches to Domain Theory have been presented in the literature (e.g. Flagg and Kopperman, Theoret. Comput.  ...  On the other hand, if the conjugate of a quasi-pseudo-metric space is hereditarily precompact, then the conjugate of the Yoneda completion is hereditarily precompact.  ...  We remark that Counterexample 1 can be adapted in order to show the precompactness of a quasi-metric space does not imply compactness of its Yoneda completion.  ... 
doi:10.1016/s0304-3975(00)00335-2 fatcat:n2tbmyzncjhahpw5sgbs4qpak4

Formal balls in fuzzy quasi-metric spaces

You Gao, Qingguo Li, Lankun Guo, Jialiang Xie
2017 Journal of Nonlinear Science and its Applications  
The notions of Yoneda completeness and Smyth completeness on fuzzy quasi-metric spaces are introduced and their relationship with other types of completeness including sequentially Yoneda completeness  ...  Then we use the standard Yoneda completeness to characterize the order-theoretical properties of the poset (BX, M ) of formal balls in a fuzzy quasi-metric space (X, M, ∧).  ...  Acknowledgment The authors are grateful to the anonymous reviewers and the area editor for their careful reading and comments. This work is supported by the NSFC (No. 11371130, 11401195)  ... 
doi:10.22436/jnsa.010.02.30 fatcat:bsnmflpibfc4hclvleadpzhhze

Page 3625 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
[Kiinzi, Hans-Peter A.] (IRL-CORK-C; Cork); Schellekens, M. P. (IRL-CORK-C; Cork) On the Yoneda completion of a quasi-metric space.  ...  They prove that the largest class of quasi-metric spaces idempotent un- 2003e:54034 der the Yoneda completion consists of the Smyth-completable spaces, where the Yoneda completion of a Smyth-completable  ... 

A Few Notes on Formal Balls [article]

Jean Goubault-Larrecq, Kok Min Ng
2017 arXiv   pre-print
Yoneda-complete quasi-metric spaces are exactly the retracts of algebraic Yoneda-complete quasi-metric spaces; every continuous Yoneda-complete quasi-metric space has a so-called quasi-ideal model, generalizing  ...  is equivalent to having enough center points; on a standard quasi-metric space, every lower semicontinuous R̅_+-valued function is the supremum of a chain of Lipschitz Yoneda-continuous maps; the continuous  ...  A quasi-metric space X, Continuous Yoneda-complete Spaces are Sober, Choquet-complete We now observe that continuous Yoneda-complete quasi-metric spaces have a number of desirable properties: they are  ... 
arXiv:1606.05445v5 fatcat:uythztg6ffhdboyhxhjm5feg6q

Computational Models of Certain Hyperspaces of Quasi-metric Spaces

Massoud Pourmahdian, Mahdi Ali-Akbari, Klaus Weihrauch
2011 Logical Methods in Computer Science  
In this paper, for a given sequentially Yoneda-complete T_1 quasi-metric space (X,d), the domain theoretic models of the hyperspace K_0(X) of nonempty compact subsets of (X,d) are studied.  ...  Next, an algebraic sequentially Yoneda-complete quasi-metric D on CBX is introduced in such a way that the specialization order _D is equivalent to the usual partial order of CBX and, furthermore, ϕ:(  ...  The authors would also like to thank two anonymous referees for their constructive comments which enabled us to correct some of the results and improve the presentation of the paper.  ... 
doi:10.2168/lmcs-7(4:1)2011 fatcat:ufron34mirhojoe34jc7l7wfmu

On the structure of formal balls of the balanced quasi-metric domain of words [article]

Salvador Romaguera, Oscar Valero
2016 arXiv   pre-print
Valero introduced and studied a balanced quasi-metric on any domain of (finite and infinite) words, denoted by q_b.  ...  In this paper we show that the poset of formal balls associated to q_b has the structure of a continuous domain  ...  A T 1 quasi-metric space is Yonedacomplete if and only if it is sequentially Yoneda-complete. Proposition 1. The quasi-metric space (Σ ∞ , q b ) is Yoneda-complete. Proof.  ... 
arXiv:1607.05298v1 fatcat:gl2k35cxrnbgjlz6gltrjotrpi

Complete Quasi-Metrics for Hyperspaces, Continuous Valuations, and Previsions [article]

Jean Goubault-Larrecq
2021 arXiv   pre-print
We introduce a variant of that construction in the realm of quasi-metric spaces, and prove that it is algebraic Yoneda-complete as soon as the underlying quasi-metric space of points is algebraic Yoneda-complete  ...  To obtain our results, we prove a few other results that have independent interest, notably: continuous Yoneda-complete spaces are consonant; on a continuous Yoneda-complete space, the Scott topology on  ...  The space of quasi-lenses on X, with the d KR quasi-metric, is Yoneda-complete.  ... 
arXiv:1707.03784v8 fatcat:vb63toh5g5ctfmu4amnayd5pfq

Generalized metric spaces: Completion, topology, and powerdomains via the Yoneda embedding

M.M. Bonsangue, F. van Breugel, J.J.M.M. Rutten
1998 Theoretical Computer Science  
All constructions are formulated in terms of (a metric version of) the Yoneda (1954) embedding.  ...  Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere, 1973) .  ...  We have been able to correct all errors but one, for which indeed a counterexample was provided in the referee report: the converse of Lemma 4.4, which we believed to hold as well.  ... 
doi:10.1016/s0304-3975(97)00042-x fatcat:z3xewd6tzzf63nmkgklayqu63u

Scott approach distance on metric spaces [article]

Wei Li, Dexue Zhang
2018 arXiv   pre-print
The notion of Scott distance between points and subsets in a metric space, a metric analogy of the Scott topology on an ordered set, is introduced, making a metric space into an approach space.  ...  It is proved that the topological coreflection of the Scott distance is sandwiched between the d-Scott topology and the generalized Scott topology; and that every injective T_0 approach space is a cocomplete  ...  Acknowledgement The authors thank sincerely the referee for the thorough analysis of the paper and the very helpful comments and suggestions.  ... 
arXiv:1610.06341v3 fatcat:rtculq2ox5gelexq5egvkuy6zu

Weighted colimits and formal balls in generalized metric spaces

J.J.M.M. Rutten
1998 Topology and its Applications  
(b) The dual of the space of metrical predicates ('fuzzy subsets') of a metric space is shown to contain the collection _?  ...  For an ordinary metric space X, the subspace of minimal elements of F is isometric to X by the co-Yoneda embedding. 0 1998 Elsevier Science B.V. All rights reserved.  ...  Acknowledgements Many thanks to Franck van Breugel, Reinhold Heckmann, and Kim Wagner for their comments on an earlier version of this paper.  ... 
doi:10.1016/s0166-8641(97)00224-1 fatcat:auoisfth4zfejb3pqa6lt7qkwu

Cauchy completion of fuzzy quasi-uniform spaces

Yongchao Wang, Yueli Yue
2021 Filomat  
In this paper, we study the completion of fuzzy quasi-uniform spaces from a categorical point of view.  ...  Finally, we study the Cauchy completion of fuzzy quasi-uniform spaces by the Yoneda embedding.  ...  Acknowledgement The authors thank the referees gratefully for their valuable comments and suggestions which help improve the paper significantly.  ... 
doi:10.2298/fil2112983w fatcat:owjfkj5fujbgvddvriynfpwk4a

A Solution to the Completion Problem for Quasi-Pseudometric Spaces

Athanasios Andrikopoulos
2013 International Journal of Mathematics and Mathematical Sciences  
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. 0 quasi-pseudometric spaces should  ...  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  ...  Similarly to what is in the theory of metric spaces, the categorical notion of a 0 quasi-pseudometric completion is the following: a complete 0 quasi-pseudometric space (̃,̃) is called a -completion of  ... 
doi:10.1155/2013/278381 fatcat:fy3lpu5yvzdthmsuk56yu7n2rm

Sober metric approach spaces [article]

Wei Li, Dexue Zhang
2017 arXiv   pre-print
It is proved that a metric space is sober, as an approach space, if and only if it is Smyth complete.  ...  Acknowledgement The authors thank cordially the referee for her/his most valuable comments and helpful suggestions.  ...  Proposition 4. 5 . 5 The underlying order of a Yoneda complete metric space is directed complete.  ... 
arXiv:1607.03208v2 fatcat:3jw7sszswfe6lhmra4igrpegwa

On the completion monad via the Yoneda embedding in quasi-uniform spaces

Maria Manuel Clementino, Dirk Hofmann
2011 Topology and its Applications  
a r t i c l e i n f o a b s t r a c t Dedicated to Eraldo Giuli on the occasion of his seventieth birthday MSC: 54B30 54E15 18D20 18C15 Keywords: Prorelation Promodule Yoneda embedding Quasi-uniform space  ...  define the Yoneda embedding, prove a (weak) Yoneda Lemma, and apply them to describe the Cauchy completion monad for quasi-uniform spaces.  ...  Here we construct a Yoneda embedding for quasi-uniform spaces, which allows us to construct the Cauchy completion in the language of modules.  ... 
doi:10.1016/j.topol.2011.01.026 fatcat:rtzizbj4v5chpmhkv2sfbmk6te

Algebraic cohomology of topological groups

David Wigner
1973 Transactions of the American Mathematical Society  
We show that topological G-modules form a quasi-abelian category in the sense of Yoneda [9], and define H { (G, A) =Ext*(Z, A) where Ext is given by the definition of Yoneda for the quasi-abelian category  ...  If A is a G-module consider the sheaf of germs of A -valued functions on each space of this semisimplicial resolution.  ...  If G is a connected Lie group, and A a finite dimensional vector space which is a differentiable G-module t then H^G, A)^Hu Q (<3, X, A); the latter is the cohomology of the Lie algebra 9 of G modulo the  ... 
doi:10.1090/s0002-9947-1973-0338132-7 fatcat:g4p5j3vmfjgd3pav6zlxux4ple
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