In this paper we introduce various notions of continuous fuzzy proper functions by using the existing notions of fuzzy closure and fuzzy interior operators like Rτ -closure, Rτ -interior, etc., and present all possible relations among these types of continuities. Next, we introduce the concepts of α-quasi-coincidence, qα r -pre-neighborhood, qα r -pre-closure and qα r pre-continuous function in...

A subset Y of a space X is Gδ-dense if it intersects every nonempty Gδ-set. The Gδ-closure of Y in X is the largest subspace of X in which Y is Gδ-dense. The space X has a regular Gδ-diagonal if the diagonal of X is the intersection of countably many regular-closed subsets of X ×X. Consider now these results: (a) [N. Noble, 1972] every Gδ-dense subspace in a product of separable metric spaces i...

This paper is concerned with the relationship between contexts, closure spaces, and complete lattices. It is shown that, for a unital quantale L, both formal concept lattices and property oriented concept lattices are functorial from the category L-Ctx of L-contexts and infomorphisms to the category L-Sup of complete L-lattices and suprema-preserving maps. Moreover, the formal concept lattice f...

Abstract: Let R be an open equivalence relation on a topological space E. We define on E a new equivalence relation ̃︀ R by x̃︀ Ry if the closure of the R-trajectory of x is equal to the closure of the R-trajectory of y. The quotient space E/̃︀ R is called the trajectory class space. In this paper, we show that the space E/̃︀ R is a simple model of the quotient space E/R. This model can provide a f...

A new definition of boundedness of linear order-homomorphisms (LOH)in $L$-topological vector spaces is proposed. The new definition iscompared with the previous one given by Fang [The continuity offuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997)829$-$838]. In addition, the relationship between boundedness andcontinuity of LOHs is discussed. Finally, a new uniform boundednessprincipl...

in this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. also, we give anew generalization of the mazur-ulam theorem when $x$ is a $2$-fuzzy $2$%-normed linear space or $im (x)$ is a fuzzy $2$-normed linear space, thatis, the mazur-ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...

The sequential spaces dealt with in the paper have arbitrary ordinals as domains of sequences and are subjected, besides the axiom of convergence of constant sequences, to only one other, quite special axiom. Categories of these sequential spaces are studied and the results are then applied to categories of associated closure spaces. It is a usual way to deene a topological structure on a set X...

Recently, the general topology has become the appropriated frame for every collection related to relations because topology is required not only for mathematics and physics but also for biology, rough set theory, biochemistry, and dynamics. In this paper, we have introduced another concept of the closure operator. In so doing, the idempotent condition, which has never been realized, is achieved...

Because antimatroid closure spaces satisfy the anti-exchange axiom, it is easy to show that they are uniquely generated. That is, the minimal set of elements determining a closed set is unique. A prime example is a discrete geometry in Euclidean space where closed sets are uniquely generated by their extreme points. But, many of the geometries arising in computer science, e.g. the world wide we...

We develop the concept of a \closure space" which appears with diierent names in many aspects of graph theory. We show that acyclic graphs can be almost characterized by the partition coeecients of their associated closure spaces. The resulting nearly total ordering of all acyclic graphs (or partial orders) provides an eeective isomorphism lter and the basis for eecient retrieval in secondary s...