Cowellpoweredness and closure operators in categories of coarse spaces

Zava, Nicolò

doi:10.1016/j.topol.2019.106899

Cited by 9 publications

(5 citation statements)

References 18 publications

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“…Moreover, we characterised in [9] both the monomorphisms and the epimorphisms of Coarse/ ∼ , showing that it is a balanced category. In [39] this study is pushed further, establishing, among others, cowellpoweredness of Coarse/ ∼ .…”

Section: Introductionmentioning

confidence: 76%

Categories of coarse groups: Quasi-homomorphisms and functorial coarse structures

Dikranjan

Zava

2020

Topology and its Applications

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Coarse geometry is the study of large-scale properties of spaces. In this paper we study group coarse structures (i.e., coarse structures on groups that agree with the algebraic structures), by using group ideals. We introduce a large class of examples of group coarse structures induced by cardinal invariants. In order to enhance the categorical treatment of the subject, we use quasihomomorphisms, as a large-scale counterpart of homomorphisms. In particular, the localisation of a category plays a fundamental role. We then define the notion of functorial coarse structures and we give various examples of those structures.

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Section: Introductionmentioning

confidence: 76%

Categories of coarse groups: Quasi-homomorphisms and functorial coarse structures

Dikranjan

Zava

2020

Topology and its Applications

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“…Corresponding notions of completeness in Category Theory were investigated in [19,25,26,28,29,40]. In particular, closure operators in different categories were studied in [16,17,18,22,30,54,55].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Absolutely closed semigroups

Банах¹,

Bardyla²

2022

Preprint

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Let C be a class of topological semigroups. A semigroupLet T1S, T2S, and TzS be the classes of T1, Hausdorff, and Tychonoff zero-dimensional topological semigroups, respectively. We prove that any ideally (resp. injectively) TzS-closed semigroup has group-bounded (resp. group-finite) center Z(X). If a viable semigroup X is ideally TzS-closed, then (1) each maximal subgroup He of X is projectively TzS-closed, (2) X contains no strictly decreasing chains of idempotents, (3) the center Z(X) of X is chain-finite, group-bounded and Clifford+finite, (4) Z(X) is projectively T1S-closed. A commutative semigroup X is absolutely TzS-closed if and only if X is absolutely T2S-closed if and only if X is chain-finite, bounded, group-finite and Clifford+finite. On the other hand, a commutative semigroup X is absolutely T1S-closed if and only if X is finite.

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“…Since the epimorphisms of Entou, SCoarse, QCoarse, and Coarse are surjective morphisms, those categories are cowellpowered. Moreover, in [23] it was proved that every epireflective subcategory of Coarse is cowellpowered. Hence the following question naturally arises.…”

Section: Entourage Structures On Certain Algebraic Structuresmentioning

confidence: 99%

Generalisations of coarse spaces

Zava

2019

Topology and its Applications

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Coarse geometry, the branch of topology that studies the global properties of spaces, was originally developed for metric spaces and then Roe introduced coarse structures ([21]) as a large-scale counterpart of uniformities. In the literature, there are very important generalisations of uniform spaces, such as semi-uniform and quasi-uniform spaces. In this paper, we introduce and start to study their large-scale counterparts, which generalise coarse spaces: semi-coarse spaces and quasi-coarse spaces. * MSC: 18B99, 54E15, 54E25, 54E99, 54A99.

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Cowellpoweredness and closure operators in categories of coarse spaces

Cited by 9 publications

References 18 publications

Categories of coarse groups: Quasi-homomorphisms and functorial coarse structures

Categories of coarse groups: Quasi-homomorphisms and functorial coarse structures

Absolutely closed semigroups

Generalisations of coarse spaces

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