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On the Yoneda completion of a quasi-metric space
2002
Theoretical Computer Science
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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
2017
Journal of Nonlinear Science and its Applications
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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
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The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
[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]
2017
arXiv
pre-print
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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
2011
Logical Methods in Computer Science
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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]
2016
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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
1998
Theoretical Computer Science
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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]
2018
arXiv
pre-print
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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
1998
Topology and its Applications
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(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
2021
Filomat
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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
2013
International Journal of Mathematics and Mathematical Sciences
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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]
2017
arXiv
pre-print
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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
2011
Topology and its Applications
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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
1973
Transactions of the American Mathematical Society
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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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