Results 1 to 10 of about 197 (158)
On finest unitary extensions of topological monoids
Topological Algebra and Its Applications, 2015 We prove that the Wyler completion of the unitary Cauchy space on a given Hausdorff topological 5 monoid consisting of the underlying set of this monoid and of the family of unitary Cauchy filters on it, is a T2-topological space and, in the commutative ...
Averbukh Boris G.
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On unitary Cauchy filters on topological monoids
Topological Algebra and Its Applications, 2013 AbstractFor Hausdorff topological monoids, the concept of a unitary Cauchy net is a generalization of the concept of a fundamental sequence of reals. We consider properties and applications of such nets and of corresponding filters and prove, in particular, that the underlying set of a given monoid, endowed with the family of such filters, forms a ...
Averbukh Boris G.
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Topological Methods for Studying Contextuality: N-Cycle Scenarios and Beyond [PDF]
Entropy, 2023 Simplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize nonsignaling distributions on contextuality scenarios.
Aziz Kharoof, Selman Ipek, Cihan Okay
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On topologies on the underlying set of a topological monoid induced by its unitary extensions
Topological Algebra and Its Applications, 2022 Extensions of a given topological monoid where all its unitary Cauchy filters converge, can induce di˙erent topologies on its underlying set. We study properties of these topologies and prove a condition under which the initial topology of this monoid is
Averbukh Boris G.
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A Topological Groupoid Representing the Topos of Presheaves on a Monoid [PDF]
Applied Categorical Structures, 2020 Butz and Moerdijk famously showed that every (Grothendieck) topos with enough points is equivalent to the category of sheaves on some topological groupoid. We give an alternative, more algebraic construction in the special case of a topos of presheaves on an arbitrary monoid. If the monoid is embeddable in a group, the resulting topological groupoid is
Jens Hemelaer
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Kuratowski Monoids of n-Topological Spaces [PDF]
Topological Algebra and its Applications, 2018 Generalizing the famous 14-set closure-complement Theorem of Kuratowski from 1922, we prove that for a set X endowed with n pairwise comparable topologies Ʈ1 ⊂ · · · ⊂ Ʈn, by repeated application of the operations of complement and closure in the ...
Banakh Taras +5 more
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A criterion of the existence of an embedding of a monothetic monoid into a topological group
Topological Algebra and Its Applications, 2019 Using properties of unitary Cauchy filters on monothetic monoids, we prove a criterion of the existence of an embedding of such a monoid into a topological group.
Averbukh Boris G.
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On unitary extensions and unitary completions of topological monoids
Topological Algebra and Its Applications, 2016 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.
Averbukh Boris G.
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Cognitive near-singularity: a possibility theorem and a witness-based protocol with a corpus case study [PDF]
Frontiers in Artificial IntelligenceObjectiveWe introduce the Cognitive Near-Singularity (CNS) as a falsifiable phase transition in reasoning systems: the regime in which updates are globally contracting, closed under composition, and invariant to benign reparameterizations, so that ...
Andy E. Williams, Andy E. Williams
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Alexandroff topologies and monoid actions
Forum Mathematicum, 2020 Abstract Given a monoid S acting (on the left) on a set X, all the subsets of X which are invariant with respect to such an action constitute the family of the closed subsets of an Alexandroff topology on X. Conversely, we prove that any Alexandroff topology may be obtained through a monoid action.
Federico Giovanni Infusino +1 more
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