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On the Yoneda completion of a quasi-metric space

2002
*
Theoretical Computer Science
*

Several theories aimed at reconciling

doi:10.1016/s0304-3975(00)00335-2
fatcat:n2tbmyzncjhahpw5sgbs4qpak4
*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*. ...##
###
Formal balls in fuzzy quasi-metric spaces

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) ...

##
###
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]

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 ...

##
###
Computational Models of Certain Hyperspaces of Quasi-metric Spaces

2011
*
Logical Methods in Computer Science
*

In this paper, for

doi:10.2168/lmcs-7(4:1)2011
fatcat:ufron34mirhojoe34jc7l7wfmu
*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. ...##
###
On the structure of formal balls of the balanced quasi-metric domain of words
[article]

2016
*
arXiv
*
pre-print

Valero introduced and studied

arXiv:1607.05298v1
fatcat:gl2k35cxrnbgjlz6gltrjotrpi
*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. ...##
###
Complete Quasi-Metrics for Hyperspaces, Continuous Valuations, and Previsions
[article]

2021
*
arXiv
*
pre-print

We introduce

arXiv:1707.03784v8
fatcat:vb63toh5g5ctfmu4amnayd5pfq
*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*. ...##
###
Generalized metric spaces: Completion, topology, and powerdomains via the Yoneda embedding

1998
*
Theoretical Computer Science
*

All constructions are formulated in terms

doi:10.1016/s0304-3975(97)00042-x
fatcat:z3xewd6tzzf63nmkgklayqu63u
*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. ...##
###
Scott approach distance on metric spaces
[article]

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. ...

##
###
Weighted colimits and formal balls in generalized metric spaces

1998
*
Topology and its Applications
*

(b)

doi:10.1016/s0166-8641(97)00224-1
fatcat:auoisfth4zfejb3pqa6lt7qkwu
*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. ...##
###
Cauchy completion of fuzzy quasi-uniform spaces

2021
*
Filomat
*

In this paper, we study

doi:10.2298/fil2112983w
fatcat:owjfkj5fujbgvddvriynfpwk4a
*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. ...##
###
A Solution to the Completion Problem for Quasi-Pseudometric Spaces

2013
*
International Journal of Mathematics and Mathematical Sciences
*

This new

doi:10.1155/2013/278381
fatcat:fy3lpu5yvzdthmsuk56yu7n2rm
*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*...##
###
Sober metric approach spaces
[article]

2017
*
arXiv
*
pre-print

It is proved that

arXiv:1607.03208v2
fatcat:3jw7sszswfe6lhmra4igrpegwa
*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*. ...##
###
On the completion monad via the Yoneda embedding in quasi-uniform spaces

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. ...

##
###
Algebraic cohomology of topological groups

1973
*
Transactions of the American Mathematical Society
*

We show that topological G-modules form

doi:10.1090/s0002-9947-1973-0338132-7
fatcat:g4p5j3vmfjgd3pav6zlxux4ple
*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*...
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