Transformations of Discrete Closure Systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F13%3APU98352" target="_blank" >RIV/00216305:26210/13:PU98352 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Transformations of Discrete Closure Systems

Popis výsledku v původním jazyce

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 assert

Název v anglickém jazyce

Transformations of Discrete Closure Systems

Popis výsledku anglicky

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 assert

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: Centrum excelence IT4Innovations</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Acta Mathematica Hungarica

ISSN

0236-5294

e-ISSN

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Svazek periodika

138

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

HU - Maďarsko

Počet stran výsledku

20

Strana od-do

386-405

Kód UT WoS článku

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EID výsledku v databázi Scopus

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