相关论文: On Regular Closure Operators and Cowellpowered Sub…

We give some applications of closure operators in category of groups and link them with the join problem of subnormal subgroups.

In this article the notions of (quasi weakly hereditary) general closure operator $\mb{C}$ on a category $\cx$ with respect to a class $\cm$ of morphisms, and quasi factorization structures in a category $\cx$ are introduced. It is shown…

The paper is devoted to counterexamples involving the triviality of domains of products and/or adjoints of densely defined operators.

In this article we give application of closure operators in category of modules. Our main result shows that every subcategory A of injective modules of R-mod (under a mild condition) induces a torsion theory of R-mod.

A theorem is derived which (i) provides a new class of subfactors which may be interpreted as generalized asymptotic subfactors, and which (ii) ensures the existence of two-dimensional local quantum field theories associated with certain…

We study a regular closure operator in the category of quandles. We show that the regular closure operator and the pullback closure operator corresponding to the reflector from the category of quandles to its full subcategory of trivial…

In this paper we investigate the interplay between isolated suborders and closures. Isolated suborders are a special kind of suborders and can be used to diminish the number of elements of an ordered set by means of a quotient construction.…

A folklore result in category theory is that a (weakly) Cartesian closed category with finite co-products is distributive. Usually, the proof of this small result is carried on using the fact that the exponential functor is right adjoint to…

An expansive, monotone operator is dominating; if it is also idempotent it is a closure operator. Although they have distinct properties, these two kinds of discrete operators are also intertwined. Every closure operator is dominating;…

Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no…

Internal preneighbourhood spaces inside any finitely complete category with finite coproducts and proper factorisation structure were first introduced in my earlier paper. This paper proposes a closure operation on internal preneighbourhood…

We show that algebraic formulas and constant-depth circuits are closed under taking factors. In other words, we show that if a multivariate polynomial over a field of characteristic zero has a small constant-depth circuit or formula, then…

A notion of tail dependence based on operator regular variation is introduced for copulas, and the standard tail dependence used in the copula literature is included as a special case. The non-standard tail dependence with marginal power…

Non-closedness of subexponentiality by the convolution operation is well-known. We go a step further and show that subexponentiality and non-subexponentiality are generally changeable by the convolution. We also give several conditions, by…

We show that factorization systems, both strict and orthogonal, can be equivalently described as double categories satisfying certain properties. This provides conceptual reasons for why the category of sets and partial maps or the category…

We study a closure operator derived from the matrix endofunctor on the category of rings with unity. We investigate the invariance of various ring-theoretic properties under this operator. A key finding is the decisive nature of this…

In this note, a condition (\emph{open persistence}) is presented under which a (pre)closure operation on submodules (resp. ideals) over rings of global sections over a scheme $X$ can be extended to a (pre)closure operation on sheaves of…

Let $A$ and $B$ be two densely defined unbounded closeable operators in a Hilbert space such that their unbounded operator products $AB$ and $BA$ are also densely defined. Then all four operators possess adjoints and we obtain new inclusion…

The rankable and compressible sets have been studied for more than a quarter of a century, ever since Allender [1] and Goldberg and Sipser [6] introduced the formal study of polynomial-time ranking. Yet even after all that time, whether the…

We study connections between closure operators on an algebra $(A,\Om)$ and congruences on the extended power algebra defined on the same algebra. We use these connections to give an alternative description of the lattice of all subvarieties…