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}^{...

Abstract. The topological structure of the QCD vacuum can be probed by monitoring the spatial localization of the low-lying Dirac eigenmodes. This approach can be pursued on the lattice, and unlike the traditional one requires no smoothing of the gauge field. I review recent lattice studies, attempting to extract a consistent description. What emerges is a picture of the vacuum as a “topologica...

In this paper we introduce a new definition of a lattice fuzzy topology which is a generalization of Lowen’s fuzzy topology and show that the category of Lowen’s fuzzy topological spaces is a bireflective full subcategory of the category of lattice fuzzy topological spaces.

in this paper we construct the category of coverings of fundamental generalized lie group-groupoid associatedwith a connected generalized lie group. we show that this category is equivalent to the category of coverings of aconnected generalized lie group. in addition, we prove the category of coverings of generalized lie groupgroupoidand the category of actions of this generalized lie group-gro...

Topological control of nanostructures plays a crucial role in understanding the crystal growth process at the nanometer length scale. Here, the scalable synthesis of upconversion materials with distinct hedgehog-like morphologies by a seed-mediated synthetic procedure is reported. It is demonstrated that a close match in the crystal lattice between the core and shell components is essential for...

Topological concepts have been applied to a wide range of fields in order successfully describe the emergence robust edge modes that are unaffected by scattering or disorder. In photonics, indications lasing from topologically protected with improved overall laser characteristics were observed. Here, we study exciton-polariton microcavity traps arranged one-dimensional Su-Schrieffer-Heeger latt...

The aim of this paper is to introduce the concept of generalized regular closed sets and study some of its properties . The corresponding topological space formed by the family of these sets is also studied. It may be noted that regular closed set doesn’t forms even a supra topological space. Various researchers had studied the concept of generalized closed sets and regular generalized closed s...

Let T be a topological space and let A be a subset of T . Recall that A is said to be a closed domain of T if A = IntA and A is said to be an open domain of T if A = IntA (see e.g. [8], [15]). Some simple generalization of these notions is the following one. A is said to be a domain of T provided IntA ⊆ A ⊆ IntA (see [15] and compare [7]). In this paper certain connections between these concept...