منابع مشابه
From torsion theories to closure operators and factorization systems
Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].
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We introduce fuzzy closure systems and fuzzy closure operators as extensions of closure systems and closure operators. We study relationships between fuzzy closure systems and fuzzy closure spaces. In particular, two families F (S) and F (C) of fuzzy closure systems and fuzzy closure operators on X are complete lattice isomorphic.
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In an 〈E,M 〉-category X for sinks, we identify necessary conditions for Galois connections from the power collection of the class of (composable pairs) of morphisms in M to factor through the “lattice” of all closure operators on M , and to factor through certain sublattices. This leads to the notion of regular closure operator. As one byproduct of these results we not only arrive (in a novel w...
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متن کاملClosure Operators and Subalgebras1
In this article we present several logical schemes. The scheme SubrelstrEx deals with a non empty relational structure A , a set B, and a unary predicate P , and states that: There exists a non empty full strict relational substructure S of A such that for every element x of A holds x is an element of S if and only if P [x] provided the following conditions are met: • P [B], and • B ∈ the carri...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1975
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700031530