Closure theories of powerset theories

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Closure theories of powerset theories

Popis výsledku v původním jazyce

A notion of a closure theory of a powerset theory in a ground category is introduced as a generalization of a topology theory of a powerset the- ory. Using examples of powerset theories in the category Set of sets and in the category of sets with similarity relations, it is proved that these theories can be used as ground theories for closure theories of powerset theories in these two categories. Moreover, it is proved that all these clo- sure theories of powerset theories are topological constructs. Anotion of a closure operator which preserves a canonical form of fuzzy objects in these categories is introduced, and it is proved that a closure theory of a powerset theory in the ground category Set is a core ective subcategory of the closure theory of(Zadeh's) powerset theory, which preserves canonical forms of fuzzy sets.

Název v anglickém jazyce

Closure theories of powerset theories

Popis výsledku anglicky

A notion of a closure theory of a powerset theory in a ground category is introduced as a generalization of a topology theory of a powerset the- ory. Using examples of powerset theories in the category Set of sets and in the category of sets with similarity relations, it is proved that these theories can be used as ground theories for closure theories of powerset theories in these two categories. Moreover, it is proved that all these clo- sure theories of powerset theories are topological constructs. Anotion of a closure operator which preserves a canonical form of fuzzy objects in these categories is introduced, and it is proved that a closure theory of a powerset theory in the ground category Set is a core ective subcategory of the closure theory of(Zadeh's) powerset theory, which preserves canonical forms of fuzzy sets.

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

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Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Tatra Mountains Mathematical Publications

ISSN

1210-3195

e-ISSN

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Svazek periodika

64

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

SK - Slovenská republika

Počet stran výsledku

25

Strana od-do

101-126

Kód UT WoS článku

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EID výsledku v databázi Scopus

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