The Experts below are selected from a list of 357 Experts worldwide ranked by ideXlab platform
Averbukh Boris G. - One of the best experts on this subject based on the ideXlab platform.
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On unitary extensions and unitary completions of topological monoids
De Gruyter, 2016Co-Authors: Averbukh Boris G.Abstract:The concept of a unitary Cauchy Net in an arbitrary Hausdorff topological monoid generalizes the concept of a fundamental sequence of reals. We construct extensions of this monoid where all its unitary Cauchy Nets converge
W U Huihua - One of the best experts on this subject based on the ideXlab platform.
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Cauchy Net and Cauchy filter in uniform space
Journal of Gansu Lianhe University, 2008Co-Authors: W U HuihuaAbstract:The relationship between limit of Cauchy Net and that of its subNet in uniform space(X,μ) is studied.The completeness of(X,μ) can be characterized by means of Cauchyness of Nets or filters.The relation of Cauchyness of Net and filter to Cauchyness of filter and Net induced by them respectively is investigated,and an equivalent relation between Cauchy Net and Cauchy filter is obtained.
Mundici D - One of the best experts on this subject based on the ideXlab platform.
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Cauchy completeness in elementary logic
'JSTOR', 2015Co-Authors: Jc Cifuentes, Am Sette, Mundici DAbstract:The inverse of the distance between two structures A not equal B of finite type sis naturally measured by the smallest integer q such that a sentence of quantifier rank q-1 is satisfied by A but not by B. In this way the space Str of structures of type tau is equipped with a pseudometric. The induced topology coincides with the elementary topology of Str(tau). Using the rudiments of the theory of uniform spaces, in this elementary note we prove the convergence of every Cauchy Net of structures, for any type tau.6141153115
Cobzaş S. - One of the best experts on this subject based on the ideXlab platform.
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Completeness in quasi-pseudometric spaces
2020Co-Authors: Cobzaş S.Abstract:The aim of this paper is to discus the relations between various notions of sequential completeness and the corresponding notions of completeness by Nets or by filters in the setting of quasi-metric spaces. We propose a new definition of right $K$-Cauchy Net in a quasi-metric space for which the corresponding completeness is equivalent to the sequential completeness. In this way we complete some results of R.~A. Stoltenberg, Proc. London Math. Soc. \textbf{17} (1967), 226--240, and V.~Gregori and J.~Ferrer, Proc. Lond. Math. Soc., III Ser., \textbf{49} (1984), 36.Comment: 19 p, entirely revised, a new notion of Cauchy Net propose
Gounaridis Ioannis - One of the best experts on this subject based on the ideXlab platform.
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On Stoltenberg's quasi-uniform completion
2020Co-Authors: Andrikopoulos Athanasios, Gounaridis IoannisAbstract:In this paper, we give a new completion for quasi-uniform spaces which generalizes the completion theories of Doitchinov [8] and Stoltenberg [20]. The presented completion theory is very well-behaved and extends the completion theory of uniform spaces in a natural way. That is, the definition of Cauchy Net and the constructed completion coincide with the classical in the case of uniform spaces. The main contribution this completion theory makes is the notion of the cut of Nets which generalize the idea of Doitchinov for the notion of-Cauchy Net [1