Transformations of Discrete Closure Systems

Result code in 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>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Transformations of Discrete Closure Systems
Original language 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 assert
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: IT4Innovations Centre of Excellence</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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