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Recursive quasi-metric spaces

2003
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Theoretical Computer Science
*

We introduce a deÿnition of

doi:10.1016/s0304-3975(02)00692-8
fatcat:nvcrnrielfavnhwbofxzytgfsu
*recursive**quasi*-*metric**spaces*in analogy to*recursive**metric**spaces*. ... We show that this concept leads to similar results as in the*metric*case and we prove that the most important*spaces*of computable analysis can be naturally considered as*recursive**quasi*-*metric**spaces*. ... K unzi for an interesting discussion on*quasi*-*metric**spaces*and non-symmetric topologies and he is grateful to the anonymous referees who provided many useful suggestions and corrections. ...##
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New results on the Baire partial quasi-metric space, fixed point theory and asymptotic complexity analysis for recursive programs

2014
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Fixed Point Theory and Applications
*

Syst. 50:387-399, 2012), on the use of partial

doi:10.1186/1687-1812-2014-14
fatcat:lg22box6o5fircjqtp63mt7s7i
*quasi*-*metric**spaces*for asymptotic complexity analysis of algorithms. ... Syst. 50:387-399, 2012), a new mathematical fixed point technique, that uses the so-called Baire partial*quasi*-*metric**space*, was introduced with the aim of providing the asymptotic complexity of a class ... Moreover, a partial*quasi*-*metric**space*(X, q) is said to be complete provided that the associated*quasi*-*metric**space*(X, d q ) is bicomplete. ...##
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A Common Mathematical Framework for Asymptotic Complexity Analysis and Denotational Semantics for Recursive Programs Based on Complexity Spaces
[chapter]

2012
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Semantics - Advances in Theories and Mathematical Models
*

A

doi:10.5772/36799
fatcat:cdksmgzsbfapvlpqqqvohj3vdy
*quasi*-*metric**space*is a pair (X, d) such that X is a nonempty set and d is a*quasi*-*metric*on X. ... A*quasi*-*metric**space*(X, d) is called bicomplete whenever the*metric**space*(X, d s ) is complete. ...##
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The complexity space of partial functions: a connection between complexity analysis and denotational semantics

2011
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International Journal of Computer Mathematics
*

An extension of the complexity

doi:10.1080/00207161003631885
fatcat:kggahaxodbh47okydoa4xrxav4
*space*of partial functions is constructed in order to give a mathematical model for the validation of*recursive*definitions of programs. ... The study of dual complexity*spaces*, introduced by S. Romaguera and M. ... An extended*quasi*-*metric**space*is a pair (X, d) such that X is a (nonempty) set and d is an extended*quasi*-*metric*on X. ...##
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Families of Riemann surfaces and Weil-Petersson geometry
[article]

2012
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arXiv
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pre-print

Brock discovered that Teichmüller

arXiv:1202.4078v1
fatcat:iupc525kpzd7dialvhaegfk6xy
*space*with the WP*metric*is*quasi*isometric to P (R) with the unit-edge*metric*, [Bro03] . ... As above the augmented Teichmüller*space*T is a CAT (0)*metric**space*with T , T*quasi*isometric to the pants graph P (R). Recently the Alexandrov tangent cones of T have been described, [Wlp08] . ...##
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Effective Banach spaces
[article]

2012
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arXiv
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pre-print

The example given is a structure on the Banach

arXiv:1207.6622v1
fatcat:etnez7t77fclhisewd56picpca
*space*of bounded linear operators on the set of almost periodic functions. ... This thesis addresses Pour-El and Richards' fourth question from their book "Computability in analysis and physics", concerning the relation between higher order*recursion*theory and computability in analysis ...*Quasi*-effectivity and r.e.-indices*Quasi*-numbering of X k corresponds to a numbering of the*recursive*sets using r.e.-indices. ...##
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Distortion of leaves in product foliations

2002
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Topology and its Applications
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That is, the function which compares intrinsic distances in leaves with extrinsic distances in the ambient

doi:10.1016/s0166-8641(01)00231-0
fatcat:n5lmw2kdfjdb3gmh2gmigaosx4
*space*grows faster than any*recursive*function. ... We produce examples of codimension one foliations of H 2 and E 2 with bounded geometry which are topologically product foliations, but for which leaves are non-*recursively*distorted. ... A decorated*metric**space*is a*metric**space*in the usual sense with some auxiliary structure. ...##
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Generalized α-ψ contractive mappings in quasi-metric spaces and related fixed-point theorems

2014
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Journal of Inequalities and Applications
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Remark A sequence {x n } in a

doi:10.1186/1029-242x-2014-36
fatcat:vocomxxcsbdu3cs5c7vlb2hcdq
*quasi*-*metric**space*is Cauchy if and only if it is left-Cauchy and right-Cauchy. Definition Let (X, d) be a*quasi*-*metric**space*. ... Definition Let (X, d) be a*quasi*-*metric**space*and T : X → X be a given mapping. ... Then d called a*quasi*-*metric*and the pair (X, d) is called a*quasi*-*metric**space*. Remark Any*metric**space*is a*quasi*-*metric**space*, but the converse is not true in general. ...##
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Page 594 of Mathematical Reviews Vol. 41, Issue 3
[page]

1971
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Mathematical Reviews
*

extension of a quantificational logic.

*metric**space*to a complete*metric**space*) a*quasi*-*metric*J. ... possible vari- | mappings from*quasi*-*metric**spaces*into*quasi*-*metric*ables as objects of the subject domain). ...##
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New results on the mathematical foundations of asymptotic complexity analysis of algorithms via complexity spaces

2012
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International Journal of Computer Mathematics
*

that solves the problem of Hanoi Towers.

doi:10.1080/00207160.2012.659246
fatcat:ebezdojscrbdhgykzqblqcrxhu
*quasi*-*metric*, complexity*space*, fixed point, improver, worsener, complexity class, Quicksort, Hanoi, Largetwo. ... Schellekens introduced the theory of complexity (*quasi*-*metric*)*spaces*as a part of the development of a topological foundation for the asymptotic complexity analysis of programs and algorithms [Electron ... A*quasi*-*metric**space*(X, d) is called bicomplete if the*metric**space*(X, d s ) is complete. ...##
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Page 4532 of Mathematical Reviews Vol. , Issue 93h
[page]

1993
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Mathematical Reviews
*

Smyth begins by considering

*quasi*-*metric*and*quasi*-uniform*spaces*(where, as in the preceding paper, “*quasi*” means that symmetry is not required), showing that the assumption of total boundedness leads ... De Bakker and Rutten use*metric**spaces*as semantical domains. They work with a category of*metric**spaces*, where the morphisms are isometric injections with distance-nonincreasing retractions. ...##
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Page 7281 of Mathematical Reviews Vol. , Issue 2001J
[page]

2001
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Mathematical Reviews
*

of

*metric**spaces*(*recursive*conditions for*spaces*at work). ... As a by-product it is shown that a quasimetrizable Moore*space*admits a left K- complete*quasi*-*metric*if and only if it is a complete Aronszajn*space*.” 2001j:54012 54C35 54C08 54E35 McCoy, R. A. ...##
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Nonexistence of Quasi-Invariant Measures on Infinite-Dimensional Linear Spaces

1966
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Proceedings of the American Mathematical Society
*

These will both follow if it can be shown that X is a separable

doi:10.2307/2035076
fatcat:x5cc23knqng6dcgsrgxgh2yppy
*metric**space*, which we do by exhibiting a countable dense subset. Let 5B(x) be the open 1/w-sphere about x, in some fixed*metric*. ... Sudakov [7] that a locally convex topological linear*space*with a nontrivial*quasi*-invariant <r-finite measure on its weakly measurable sets must be finite-dimensional. ... We wish to show the*recursive*unsolvability of primitive*recursive*arithmetic (PRA). ...##
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Weil-Petersson perspectives
[article]

2005
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arXiv
*
pre-print

We highlight recent progresses in the study of the Weil-Petersson (WP) geometry of finite dimensional Teichmüller

arXiv:math/0502519v2
fatcat:33sf6wsfdfdmthhxzvn2443uby
*spaces*. ... For recent progress on and the understanding of infinite dimensional Teichmüller*spaces*the reader is directed to the recent work of Teo-Takhtajan. ... A more general matter is to understand the behavior of*quasi*-geodesics and especially*quasi*-flats,*quasi*-isometric embeddings of Euclidean*space*into T . ...##
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Enumeration Degrees and Topology
[chapter]

2018
*
Lecture Notes in Computer Science
*

, a slightly different effectivization of

doi:10.1007/978-3-319-94418-0_33
fatcat:udwtkxjcozeezeltcj6nxo5kwi
*metric**spaces*is used, namely*recursively*presented*metric**spaces*. ... The complete version of countably-based T 0*spaces*are the*quasi*-Polish*spaces*[4] . The generalized reducibility restricted to computable*metric**spaces*was studied by Miller [30] . ...
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