7 Results Found

The notion of convergence wins its own important part in the branch of Topology. Convergences in metric spaces, topological spaces, fuzzy topological spaces, fuzzy metric spaces, partially ordered sets (in short, posets), and fuzzy ordered sets (in s...

This paper introduces and investigates a new class of generalized open sets, called fuzzy $h_{\mathcal{I}}$-open sets, in fuzzy ideal topological spaces $(X,\tilde{\tau },\tilde{\mathcal{I}})$. We prove that the collection of all fuzzy $h_{\mathcal{I}}$-open sets forms a fuzzy topology ${\stackrel{\&t}{\tau }}^{}$...

In this paper, we introduce the notion of $\left(p,q\right)$-fuzzy local function and DF-ideal topological space. Also, we introduce the concepts DFU-ð-continuous and DFL-ð-continuous, almost ð-continuous, weakly ð-continuous and almost weakly ð...

This paper is devoted to the study of the interrelationships among $\mathcal{LF}$-grills, $\mathcal{LF}$-ideals, $\mathcal{LF}$-neighborhoods, $\mathcal{LF}$-topologies, and $\mathcal{LF}$-co-topologies. We establish a categorical framework that demonstrates the interconnections among these concepts. In addit...

This article discusses a variety of important notions, including ideal convergence and ideal Cauchyness of topological sequences produced by fuzzy normed spaces. Furthermore, the connections between the concepts of the ideal limit and ideal cluster p...

Neutrosophy is a recent section of philosophy. It was initiated in 1980 by Smarandache. It was presented as the study of origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. In this paper, we int...

We equip a topological space $(X,\tau )$ with a function $\mathfrak{a}:X\to \tau$ satisfying the single axiom $x\in \mathfrak{a}\left(x\right)$. The resulting triple $(X,\tau ,\mathfrak{a})$, which we call an aura topological space, provides a point-to-open-set assignment that differs from all ex...