About: Transformations of Discrete Closure Systems

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Discrete systems such as sets, monoids, groups are familiar categories. The internal structure of the latter two is defined by an algebraic operator. In this paper we concentrate on discrete systems that are characterized by unary operators; these include choice operators $\CHOICE$, encountered in economics and social theory, and closure operators $\CL$, encountered in discrete geometry and data mining. Because, for many arbitrary operators $\OPER$, it is easy to induce a closure structure on the base set, closure operators play a central role in discrete systems. Our primary interest is in functions $f$ that map power sets $2^{\UNIV}$ into power sets $2^{\UNIV'}$, which are called transformations. Functions over continuous domains are usually characterized in terms of open sets. When the domains are discrete, closed sets seem more appropriate. In particular, we consider monotone transformations which are ``continuous'', or ``closed''. These can be used to establish criteria for asserting that ``the c Discrete systems such as sets, monoids, groups are familiar categories. The internal structure of the latter two is defined by an algebraic operator. In this paper we concentrate on discrete systems that are characterized by unary operators; these include choice operators $\CHOICE$, encountered in economics and social theory, and closure operators $\CL$, encountered in discrete geometry and data mining. Because, for many arbitrary operators $\OPER$, it is easy to induce a closure structure on the base set, closure operators play a central role in discrete systems. Our primary interest is in functions $f$ that map power sets $2^{\UNIV}$ into power sets $2^{\UNIV'}$, which are called transformations. Functions over continuous domains are usually characterized in terms of open sets. When the domains are discrete, closed sets seem more appropriate. In particular, we consider monotone transformations which are ``continuous'', or ``closed''. These can be used to establish criteria for asserting that ``the c (en)
Title	Transformations of Discrete Closure Systems Transformations of Discrete Closure Systems (en)
skos:prefLabel	Transformations of Discrete Closure Systems Transformations of Discrete Closure Systems (en)
skos:notation	RIV/00216305:26210/13:PU98352!RIV14-MSM-26210___
http://linked.open...avai/predkladatel	Fakulta strojního inženýrství
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(ED1.1.00/02.0070)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Šlapal, Josef
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Vysoké učení technické v Brně / Fakulta strojního inženýrství
http://linked.open...dnocenehoVysledku	111587
http://linked.open...ai/riv/idVysledku	RIV/00216305:26210/13:PU98352
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	closure, choice, operator, continuous, category, function (en)
http://linked.open.../riv/klicoveSlovo	continuous operator choice closure category function
http://linked.open...odStatuVydavatele	HU - Maďarsko
http://linked.open...ontrolniKodProRIV	[FA34E1A9657B]
http://linked.open...i/riv/nazevZdroje	Acta Mathematica Hungarica
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	IT4Innovations Centre of Excellence
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	138
http://linked.open...iv/tvurceVysledku	Šlapal, Josef Pfaltz, John
issn	0236-5294
number of pages	20 (xsd:int)
http://localhost/t...ganizacniJednotka	26210

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