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Bohr compactifications of algebras and structures
SYS 0248444 LBL ---naa--22--------450- 005 20240104140913.5 014 $a 000401991700006 $2 WOS CC. SCIE 014 $a 2-s2.0-84975517216 $2 SCOPUS 017 70
$a 10.1007/s10485-016-9436-0 $2 DOI 100 $a 20170712a2017 m y slo 03 ba 101 0-
$a eng 102 $a NL 200 1-
$a Bohr compactifications of algebras and structures $f B. A. Davey, M. Haviar, H. A. Priestley 330 $a 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. 463 -1
$1 001 umb_un_cat*0293667 $1 011 $a 0927-2852 $1 011 $a 1572-9095 $1 200 1 $a Applied Categorical Structures $v Vol. 25, no. 3 (2017), pp. 403-430 $1 210 $a Dordrecht $c Springer $d 2017 600 -1
$3 umb_un_auth*0165306 $a Bohr $b Niels $c dánsky fyzik $f 1885-1962 606 0-
$3 umb_un_auth*0125164 $a natural duality 606 0-
$3 umb_un_auth*0197787 $a natural extension 606 0-
$3 umb_un_auth*0121524 $a distributive lattices 606 0-
$3 umb_un_auth*0261163 $a Stone-Čechova kompaktifikácia $X Stone-Čech compactification 615 $n 51 $a Matematika 675 $a 51 700 -0
$3 umb_un_auth*0003450 $a Davey $b Brian A. $9 34 $4 070 701 -0
$3 umb_un_auth*0002686 $a Haviar $b Miroslav $p UMBFP10 $4 070 $9 33 $f 1965- $T Katedra matematiky 701 -0
$3 umb_un_auth*0022288 $a Priestley $b Hilary A. $4 070 $9 33 T85 $x existuji fulltexy
Number of the records: 1