in this paper, we introduce and characterize fuzzy wea-kly $e$-closed functions in fuzzy topological spaces and the relationship between these mappings and some properties of them are investigated.

In this paper, first we prove fixed point theorems for different variant of compatible maps, satisfying a contractive condition of integral type in fuzzy metric spaces, which improve the results of Branciari [2], Rhoades [33], Kumar et al. [23], Subramanyam [35] and results of various authors cited in the literature of ”Fixed Point Theory and Applications”. Secondly, we introduce the notion of ...

{V : V ∈ Vn} = X . Clearly, every Menger space is almost Menger and every almost Menger space is weakly Menger, but the converses do not hold (see Examples 2.1 and 2.2). On the study of weakly Menger spaces, almost Menger spaces and Menger spaces, the readers can see the references [2, 3, 4, 5, 6]. Here we investigate the relationships among almost Menger spaces, weakly Menger spaces and Menger...

A labeled graph is said to be weakly bipartite if the clutter of its odd cycles is ideal. Seymour conjectured that a labeled graph is weakly bipartite if and only if it does not contain a minor called an oddK5. A proof of this conjecture is given in this paper. Let G = (V;E) be a graph and E. We call edges in odd and edges in E even. The pair (G; ) is called a labeled graph. A subset L E(G) is ...

In this paper we show that for every n ≥ 2 there are minimal systems with perfect weakly mixing sets of order n and all weakly mixing sets of order n+1 trivial. We present some relations between weakly mixing sets and topological sequence entropy, in particular, we prove that invertible minimal systems with nontrivial weakly mixing sets of order 3 always have positive topological sequence entro...

We present a design technique for binary weakly-dual codes from which we construct quantum error-correction codes (quantum codes) via the CSS technique. The weakly-dual forward error-correction (FEC) codes are based on diagonals of different slopes on a rectangular η 2 ×η array (type-R array) with η even. Some methods to increase the minimum distance of such codes are presented. Index Terms — q...