Related papers: On Nano Semi Alpha Open Sets

Here we have studied the ideas of $ sg_\lambda,s\lambda$ and $ s\beta_\lambda $-closed sets and investigated some of their properties in generalized topological spaces. We have also studied some low separation axioms namely $ s\lambda…

In this note, we consider the space $H(\Omega)^{\mathbb N}$ of sequences of holomorphic functions on an open set $\Omega\subset {\mathbb C}$. If $H(\Omega)$ is endowed with its natural topology and $H(\Omega)^{\mathbb N}$ is endowed with…

We survey some properties of homotopical and homological $Z_n$-sets in topological spaces.

In this paper, we introduce a new fractional Musielak-Sobolev space $Ws,{\Phi}x,y({\Omega})$ where ${\Omega}$ is an open subset in RN and we show some density properties of smooth and compactly supported functions in this space.

We consider a semi-algebraic function defined on a closed semi-algebraic set X. We give formulas relating the topology of X to the indices of the critical points of the function and to the topological behavior of the function at infinity.…

Let $S$ be an integral domain with field of fractions $F$ and let $A$ be an $F$-algebra. An $S$-subalgebra $R$ of $A$ is called $S$-nice if $R$ is lying over $S$ and the localization of $R$ with respect to $S \setminus \{ 0 \}$ is $A$. Let…

In this paper, we introduce soft continuous mappings which are defined over an initial universe set with a fixed set of parameters. Later we study soft open and soft closed mappings, soft homeomorphism and investigate some properties of…

This paper introduces and investigates a new class of almost normal spaces, referred to as almost SC*-normal spaces, which are defined using SC*-open sets. Building on the work of A. Chandrakala and K. Bala Deepa Arasi, we explore several…

This is a write-up of lectures on integrable sigma-models, which covers the following topics: (1) Homogeneous spaces, (2) Classical integrability of sigma-models in two dimensions, (3) Topological terms, (4) Background-field method and…

The properties of the spaces of Sugeno integrable functions are quite different from those of the ordinary spaces of Lebesgue integrable functions. The purpose of the paper is to further advance our study of the Sugeno-Lorentz spaces, in…

In this paper we further explore the L-shadowing property defined in [17] for dynamical systems on compact spaces. We prove that structurally stable diffeomorphisms and some pseudo-Anosov diffeomorphisms of the two-dimensional sphere…

This paper is devoted to a general presentation of anti-topological spaces. These structures have been initially proposed by \c{S}ahin, Karg{\i}n and M. Y\"{u}cel in 2021. We analyse their basic definition, showing some of its subtleties…

Finite topological spaces became much more essential in topology, with the development of computer science. The task of this paper is to study and investigate some properties of such spaces with the existence of an ordered relation between…

In this paper we continue to study the property of separability of functional space C(X) with the open-point and bi-point-open topologies.

For a commutative ring $R$ with unit $1\ne 0$ and a multiplicatively closed subset $S$ of $R$, we introduce a new topology on the $S$-prime spectrum $\mathrm{Spec}_SR$ of $R$ called the $S$-flat topology. Our aims is to give an algebraic…

This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fundamental group, as well as a review of known examples.

The aim of this paper is to give a unifying description of various constructions (subanalytic, semialgebraic, o-minimal site) using the notion of T-topology. We then study the category of T-sheaves.

The near field scanning optical microscopy (NSOM) is not only a tool for imaging of objects in the sub wavelength limit but also a prominent characteristic tool for understanding the intrinsic properties of the nanostructures. The effect of…

We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…

The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…