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Recursive quasi-metric spaces

Vasco Brattka
2003 Theoretical Computer Science  
We introduce a deÿnition of 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.  ... 
doi:10.1016/s0304-3975(02)00692-8 fatcat:nvcrnrielfavnhwbofxzytgfsu

New results on the Baire partial quasi-metric space, fixed point theory and asymptotic complexity analysis for recursive programs

Maryam A Alghamdi, Naseer Shahzad, Oscar Valero
2014 Fixed Point Theory and Applications  
Syst. 50:387-399, 2012), on the use of partial 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.  ... 
doi:10.1186/1687-1812-2014-14 fatcat:lg22box6o5fircjqtp63mt7s7i

A Common Mathematical Framework for Asymptotic Complexity Analysis and Denotational Semantics for Recursive Programs Based on Complexity Spaces [chapter]

Salvador Romaguera, Oscar Valero
2012 Semantics - Advances in Theories and Mathematical Models  
A 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.  ... 
doi:10.5772/36799 fatcat:cdksmgzsbfapvlpqqqvohj3vdy

The complexity space of partial functions: a connection between complexity analysis and denotational semantics

S. Romaguera, M. P. Schellekens, O. Valero
2011 International Journal of Computer Mathematics  
An extension of the complexity 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.  ... 
doi:10.1080/00207161003631885 fatcat:kggahaxodbh47okydoa4xrxav4

Families of Riemann surfaces and Weil-Petersson geometry [article]

Scott A. Wolpert
2012 arXiv   pre-print
Brock discovered that Teichmüller 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] .  ... 
arXiv:1202.4078v1 fatcat:iupc525kpzd7dialvhaegfk6xy

Effective Banach spaces [article]

Bjørn Kjos-Hanssen
2012 arXiv   pre-print
The example given is a structure on the Banach 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.  ... 
arXiv:1207.6622v1 fatcat:etnez7t77fclhisewd56picpca

Distortion of leaves in product foliations

Danny Calegari
2002 Topology and its Applications  
That is, the function which compares intrinsic distances in leaves with extrinsic distances in the ambient 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.  ... 
doi:10.1016/s0166-8641(01)00231-0 fatcat:n5lmw2kdfjdb3gmh2gmigaosx4

Generalized α-ψ contractive mappings in quasi-metric spaces and related fixed-point theorems

Nurcan Bilgili, Erdal Karapınar, Bessem Samet
2014 Journal of Inequalities and Applications  
Remark  A sequence {x n } in a 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.  ... 
doi:10.1186/1029-242x-2014-36 fatcat:vocomxxcsbdu3cs5c7vlb2hcdq

Page 594 of Mathematical Reviews Vol. 41, Issue 3 [page]

1971 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).  ... 

New results on the mathematical foundations of asymptotic complexity analysis of algorithms via complexity spaces

S. Romaguera, P. Tirado, O. Valero
2012 International Journal of Computer Mathematics  
that solves the problem of Hanoi Towers. 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.  ... 
doi:10.1080/00207160.2012.659246 fatcat:ebezdojscrbdhgykzqblqcrxhu

Page 4532 of Mathematical Reviews Vol. , Issue 93h [page]

1993 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.  ... 

Page 7281 of Mathematical Reviews Vol. , Issue 2001J [page]

2001 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.  ... 

Nonexistence of Quasi-Invariant Measures on Infinite-Dimensional Linear Spaces

Jacob Feldman
1966 Proceedings of the American Mathematical Society  
These will both follow if it can be shown that X is a separable 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).  ... 
doi:10.2307/2035076 fatcat:x5cc23knqng6dcgsrgxgh2yppy

Weil-Petersson perspectives [article]

Scott A. Wolpert
2005 arXiv   pre-print
We highlight recent progresses in the study of the Weil-Petersson (WP) geometry of finite dimensional Teichmüller 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 .  ... 
arXiv:math/0502519v2 fatcat:33sf6wsfdfdmthhxzvn2443uby

Enumeration Degrees and Topology [chapter]

Arno Pauly
2018 Lecture Notes in Computer Science  
, a slightly different effectivization of 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] .  ... 
doi:10.1007/978-3-319-94418-0_33 fatcat:udwtkxjcozeezeltcj6nxo5kwi
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