This paper addresses the question of domesticity in the context of the increasingly nomadic condition of the world population. The history of the idea of domesticity is traced and the particular case of the hearth is addressed in detail. The paper speculates as to how user-centric information and communication technology might simulate the social and cultural value held by the traditional heart...

We use convergence theory as the framework for studying Hclosed spaces and H-sets in topological spaces. From this viewpoint, it becomes clear that the property of being H-closed and the property of being an H-set in a topological space are pretopological notions. Additionally, we define a version of H-closedness for pretopological spaces and investigate the properties of such a space.

In this paper, we propose a generalized concept of openness and closedness with respect to arbitrary fuzzy relations, along with appropriate opening and closure operators. We will show that this framework includes the existing concept defined for fuzzy preorderings as well as the triangular norm-based approach to fuzzy mathematical morphology.

We prove that a binomial edge ideal of a graph G has a quadratic Gröbner basis with respect to some term order if and only if the graph G is closed with respect to a given labelling of the vertices. We also state some criteria for the closedness of a graph G that do not depend on the labelling of its vertex set.

We are concerned with some unbounded linear operators on the so-called p-adic Hilbert space Eω. Both the Closedness and the selfadjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on Eω, and the solvability of the equation Au = v where A is a linear operator on Eω. AMS subject classification. 47S10; 46S10; 47A05; 47B25.

In this article, we establish sufficient conditions for the solution sets of parametric generalized quasi-variational relation problems with the stability properties such as the upper semicontinuity, lower semi-continuity, the Hausdorff lower semicontinuity, continuity, Hausdorff continuity, and closedness. Our results improve recent existing ones in the literature. Mathematics Subject Classifi...

The concept of pairwise S-closedness in bitopological spaces has been introduced and some properties of such spaces have been studied in this paper. EY WORDS AND PHRASES. Pairwise semi-open, Pairwise almost compact, Pairwise S-closed, Pairwise regularly open and regularly closed, Pairwise extremal disconnectedness, Pairwise semi-continuous and irresolute functions. 1980 AMS MATHEMATICS SUBJECT ...

In this paper we define gradation of RS-compactness and S*-closed spaces in L-topological spaces.We generalize the degrizations of RS-compactness and S*-closedness to the L-topological space and give the positions of them under weak forms of L-continuity. 2010 AMS Classification: 54A40, 06D72

In this paper, we describe the relationships between pseudo MV algebras and semirings. We also give definitions of automata on lattice ordered semirings, prove that the family of K-Languages is closed under union, and discuss the conditions for the closedness of families of K-languages under intersection, generalized intersection and reversal operations.

this paper extends the notion of ditopology to the case where openness and closedness are given in terms of {em a priori} unrelated drading functions. the resulting notion of graded ditopology is considered both in the setting of lattices and in that textures, the relation between the two approaches being discussed in detail. interrelations between graded ditopologies and ditopologies on textur...