Authors: Slivková, Anna
Tepavčević, Andreja 
Šešelja, Branimir
Title: Sharp partial closure operator
Journal: Miskolc Mathematical Notes
Volume: 19
Issue: 1
First page: 569
Last page: 579
Issue Date: 1-Jan-2018
Rank: M23
ISSN: 1787-2405
DOI: 10.18514/MMN.2018.1972
Abstract: 
As an improvement of existing relationships among collections of sets, closure operators and posets, a particular, so called sharp partial closure operator (SPCO) is introduced. It is proved that there is always a unique SPCO corresponding to a given partial closure system. Moreover, an SPCO has the greatest domain among all partial operators corresponding to a given system. If it is a function, an SCPO is a classical closure operator. Dealing with partial closure systems, we introduce principal ones, corresponding to principal ideals of a poset and accordingly, we define principal SPCO's. Finally, we prove a representation theorem for posets in terms of principal SPCO's and principal partial closure systems.
Keywords: partial closure operator | partial closure system | centralized system
Publisher: Miskolc University Press
Project: Development of methods of computation and information processing: theory and applications 

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