we show that the lattice of all ideals of a ring $r$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. for this purpose, we introduce the concept of the generalizedcharacteristic function $chi _{s}^{r} (a)$ of a subset $a$ of a ring $r$ forfixed $r , sin [0,1] $ and show that $a$ is an ideal of $r$ if, and only if, its generalizedcharacteristic function $chi _{s}^{...

We show that the lattice of all ideals of a ring $R$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. For this purpose, we introduce the concept of the generalizedcharacteristic function $chi _{s}^{r} (A)$ of a subset $A$ of a ring $R$ forfixed $r , sin [0,1] $ and show that $A$ is an ideal of $R$ if, and only if, its generalizedcharacteristic function $chi _{s}^{...

We call A ⊂ RN intervally thin if for all x, y ∈ RN and ε > 0 there exist x′ ∈ B(x, ε), y′ ∈ B(y, ε) such that [x′, y′] ∩ A = ∅. Closed intervally thin sets behave like sets with measure zero (for example such a set cannot ”disconnect” an open connected set). Let us also mention that if the (N − 1)-dimensional Hausdorff measure of A is zero, then A is intervally thin. A function f is preconvex ...

in this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in cat(0) spaces as well as in uced banach spaces. moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...

For every tuple $d_1,\dots, d_l\geq 2,$ let $\mathbb{R}^{d_1}\otimes\cdots\otimes\mathbb{R}^{d_l}$ denote the tensor product of $\mathbb{R}^{d_i},$ $i=1,\dots,l.$ Let us by $\mathcal{B}(d)$ hyperspace centrally symmetric convex bodies in $\mathbb{R}^d,$ $d=d_1\cdots d_l,$ endowed with Hausdorff distance, and $\mathcal{B}_\otimes(d_1,\dots,d_l)$ subset consisting that are closed unit balls reaso...

In this paper, characterizations of the degree to which a mapping $mathcal{T} : L^{X}longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail.What is more, the degree to which an $L$-subset is an $L$-open set with respect to $mathcal{T}$ is introduced.Based on that, the degrees to which a mapping $f: Xlongrightarrow Y$ is continuous,open, closed or a quotient mapping with respect t...

In this paper, we define topological hyperrings and study their basic concepts which supported by illustrative examples. We show some differences between topological rings and topological hyperrings. Also, by the fundamental relation $\Gamma^{*}$, we indicate the role of complete parts (saturated subsets) and complete hyperrings in topological hyperrings and specially we show that if every (clo...

This paper is devoted to the investigation of cardinal invariants such as hereditary density, weak and Lindelöf number. The relation between spread extent space SP2(R,?(A)) permutation degree Hattori discussed. In particular, it shown that SP2(R,?S) contains a closed discrete subset cardinality c. Moreover, functor SPGn preserves homotopy retraction topological spaces. addition, we prove if spa...

This note exhibits a brief and relatively elementary approach which the author has used when time and other exigencies precluded a more conventional development. The reader is referred to the recent paper of Cesari [l], particularly §§8, 10, 11. Let x be a continuous rectifiable mapping of a closed interval {a, b] into a fixed bounded closed subset A of the En and let [¿,_i, í¿] denote a genera...