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Title Bohr compactifications of algebras and structures Author info B. A. Davey, M. Haviar, H. A. Priestley Author Davey Brian A. (34%)
Co-authors Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Priestley Hilary A. (33%)
Source document Applied Categorical Structures. Vol. 25, no. 3 (2017), pp. 403-430. - Dordrecht : Springer, 2017 Person keywords Bohr Niels dánsky fyzik 1885-1962 Keywords natural duality natural extension distributive lattices Stone-Čechova kompaktifikácia - Stone-Čech compactification Language English Country Netherlands systematics 51 Annotation This paper provides a unifying framework for a range of categorical constructions characterised by universal mapping properties, within the realm of compactifications of discrete structures. Some classic examples fit within this broad picture: the Bohr compactification of an abelian group via Pontryagin duality, the zero-dimensional Bohr compactification of a semilattice, and the Nachbin order-compactification of an ordered set. The notion of a natural extension functor is extended to suitable categories of structures and such a functor is shown to yield a reflection into an associated category of topological structures. Our principal results address reconciliation of the natural extension with the Bohr compactification or its zero-dimensional variant. In certain cases the natural extension functor and a Bohr compactification functor are the same; in others the functors have different codomains but may agree on all objects. Coincidence in the stronger sense occurs in the zero-dimensional setting precisely when the domain is a category of structures whose associated topological prevariety is standard. It occurs, in the weaker sense only, for the class of ordered sets and, as we show, also for infinitely many classes of ordered structures. Coincidence results aid understanding of Bohr-type compactifications, which are defined abstractly. Ideas from natural duality theory lead to an explicit description of the natural extension which is particularly amenable for any prevariety of algebras with a finite, dualisable, generator. Examples of such classes-often varieties-are plentiful and varied, and in many cases the associated topological prevariety is standard. Public work category ADM No. of Archival Copy 39736 Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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Title Vybrané kapitoly z teórie zväzov Par.title [Selected topies from lattice theory] Subtitle bakalárska práca Author info Daniela Guffová; vedúci bakalárskej práce: Miroslav Haviar Author Guffová Daniela 1987-
Another authors Haviar Miroslav 1965- (Školiteľ (konzultant))
Corporation Univerzita Mateja Bela . Fakulta prírodných vied . Katedra matematiky , Banská Bystrica, Slovensko Issue data Banská Bystrica , 2009. - 46 s. : grafy, tab. Note Súbežný názov angl.. - Katedra matematiky Fakulta prírodných vied Univerzita Mateja Bela v Banskej Bystrici Keywords matematika - mathematics distributívne zväzy modulárne zväzy distributive lattices modulare lattices Language Slovak Country Slovak Republic systematics 51 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xk - Kvalifikačné práce Copy count 1, currently available 0, at library only 1 
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Title Congruence-preserving functions on distributive lattices Author info Miroslav Ploščica, Miroslav Haviar Author Ploščica Miroslav (50%)
Co-authors Haviar Miroslav 1965- (50%) UMBUV01 - Ústav vedy a výskumu
Source document Algebra Universalis. Vol. 59, no. 1-2 (2008), pp. 179-196. - Cham : Springer Nature Switzerland AG, 2008 Keywords algebra - algebra distributívne zväzy distributive lattices Language English Country Switzerland systematics 512 Public work category ADE No. of Archival Copy 10178 Repercussion category GRÄTZER, George. Lattice theory : foundation. Basel : Birkhäuser Verlag AG, 2011. 613 p. ISBN 978-3-0348-0017-4.
HALAŠ, Radomír - MESIAR, Radko - PÓCS, Jozef. Congruences and the discrete Sugeno integrals on bounded distributive lattices. In Information sciences. ISSN 0020-0255, 2016, vol. 367-368, pp. 443-448.
HALAŠ, Radomír - MESIAR, Radko - PÓCS, Jozef. A new characterization of discrete Sugeno integrals on bounded distributive lattices. In ESCIM 2015 : proceedings of 7th European symposium on computational intelligence and mathematics, Cádiz, Spain October 7th-10th, 2015. Cádiz : Universidad de Cádiz, 2015. pp. 32-37.
CÉGIELSKI, Patrick - GRIGORIEFF, Serge - GUESSARIAN, Irène. Congruence preserving functions on free monoids. In Algebra universalis. ISSN 0002-5240, 2017, vol. 78, no. 3, pp. 389-406.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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