Displaying similar documents to “On finest unitary extensions of topological monoids”

On unitary extensions and unitary completions of topological monoids

Boris G. Averbukh (2016)

Topological Algebra and its Applications

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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.

Topological Interpretation of Rough Sets

Adam Grabowski (2014)

Formalized Mathematics

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Rough sets, developed by Pawlak, are an important model of incomplete or partially known information. In this article, which is essentially a continuation of [11], we characterize rough sets in terms of topological closure and interior, as the approximations have the properties of the Kuratowski operators. We decided to merge topological spaces with tolerance approximation spaces. As a testbed for our developed approach, we restated the results of Isomichi [13] (formalized in Mizar in...

Ideal-theoretic characterizations of valuation and Prüfer monoids

Franz Halter-Koch (2004)

Archivum Mathematicum

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It is well known that an integral domain is a valuation domain if and only if it possesses only one finitary ideal system (Lorenzen r -system of finite character). We prove an analogous result for root-closed (cancellative) monoids and apply it to give several new characterizations of Prüfer (multiplication) monoids and integral domains.

Left-Garside categories, self-distributivity, and braids

Patrick Dehornoy (2009)

Annales mathématiques Blaise Pascal

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In connection with the emerging theory of Garside categories, we develop the notions of a left-Garside category and of a locally left-Garside monoid. In this framework, the relationship between the self-distributivity law LD and braids amounts to the result that a certain category associated with LD is a left-Garside category, which projects onto the standard Garside category of braids. This approach leads to a realistic program for establishing the Embedding Conjecture of [Dehornoy,...

Alienation of the Jensen, Cauchy and d’Alembert Equations

Barbara Sobek (2016)

Annales Mathematicae Silesianae

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Let (S, +) be a commutative semigroup, σ : S → S be an endomorphism with σ2 = id and let K be a field of characteristic different from 2. Inspired by the problem of strong alienation of the Jensen equation and the exponential Cauchy equation, we study the solutions f, g : S → K of the functional equation f(x+y)+f(x+σ(y))+g(x+y)=2f(x)+g(x)g(y)     for  x,y∈S. f ( x + y ) + f ( x + σ ( y ) ) + g ( x + y ) = 2 f ( x ) + g ( x ) g ( y ) for x , y ∈ S . We also consider an analogous problem for the Jensen and the d’Alembert equations as well as for the d’Alembert and the exponential...