Topological vector space
View article
Revisiting thermodynamic topologies of black holes Open
A bstract In the generalized off-shell free energy landscape, black holes can be treated as thermodynamic topological defects. The local topological properties of the spacetime can be reflected by the winding numbers at the defects, while …
View article
Dynamical topological invariant after a quantum quench Open
We show how to define a dynamical topological invariant for general\none-dimensional topological systems after a quantum quench. Focusing on\ntwo-band topological insulators, we demonstrate that the reduced momentum-time\nmanifold can be v…
View article
Compactness on Soft Topological Ordered Spaces and Its Application on the Information System Open
It is well known every soft topological space induced from soft information system is soft compact. In this study, we integrate between soft compactness and partially ordered set to introduce new types of soft compactness on the finite spa…
View article
Dynamical detection of topological charges Open
We propose a generic scheme to characterize topological phases via detecting topological charges by quench dynamics. A topological charge is defined as the chirality of a monopole at Dirac or Weyl point of spin-orbit field, and topological…
View article
Characterization of topological phase transitions via topological properties of transition points Open
We study topological properties of phase transition points of topological\nquantum phase transitions by assigning a topological invariant defined on a\nclosed circle or surface surrounding the phase transition point in the\nparameter space…
View article
Wire constructions of Abelian topological phases in three or more dimensions Open
Coupled-wire constructions have proven to be useful tools to characterize Abelian and non-Abelian topological states of matter in two spatial dimensions. In many cases, their success has been complemented by the vast arsenal of other theor…
View article
On supra soft topological ordered spaces Open
In this work, we initiate the concept of supra soft topological ordered spaces which are consider as an extension of the concept of soft topological ordered spaces. We define and discuss some notions via supra soft topological ordered spac…
View article
What is topological about topological dynamics? Open
We consider various notions from the theory of dynamical systems from a topological point of view. Many of these notions can be sensibly defined either in terms of (finite) open covers or uniformities. These Hausdorff or uniform versions c…
View article
A study of topological and geometrical characteristics of new Banach sequence spaces Open
A short extract of this study is to submit a new sequence space ℓp(F(r,s)) under the domain of the matrix F(r,s) constituted by using Fibonacci sequence and non-zero real number r and s of ℓp previously defined. Additionally, we construct …
View article
Generalized Topological Molecular Lattices Open
The aim of this paper is to introduce the concept of generalized topological molecular lattices briefly GTMLs as a generalization of Wang’s topological molecular lattices TMLs, Császár’s setpoint generalized topological spaces and lattice …
View article
On a minimax theorem: an improvement, a new proof and an overview of its applications Open
Theorem 1 of [14], a minimax result for functions $f:X\times Y\to {\bf R}$, where $Y$ is a real interval, was partially extended to the case where $Y$ is a convex set in a Hausdorff topological vector space ([15], Theorem 3.2). In doing th…
View article
Topological Rough Groups Open
The concept of topological group is a simple combination of the concepts of abstract group and topological space. The purpose of this paper is to combine the concepts of topological space and rough groups; called topological rough groups o…
View article
G-connectedness in topological groups with operations Open
It is a well known fact that for a Hausdorff topological group X, the limits of convergent sequences in X define a function denoted by lim from the set of all convergent sequences in X to X. This notion has been modified by Connor and Gros…
View article
Unified characterization for higher-order topological phase transitions Open
Higher-order topological phase transitions (HOTPTs) are associated with closing either the bulk energy gap (type-I) or boundary energy gap (type-II) without changing symmetry, and conventionally, both transitions are captured in real space…
View article
The Bishop-Phelps-Bollobas property for operators between spaces of continuous functions Open
We show that the space of bounded linear operators between spaces of continuous functions on compact Hausdorff topological spaces has the Bishop-Phelps-Bollobas property. A similar result is also proved for the class of compact operators f…
View article
A 27-Intersection Model for Representing Detailed Topological Relations between Spatial Objects in Two-Dimensional Space Open
Determining the spatial relations between objects is a primary function of a geographic information system (GIS). One important aspect of spatial relations is topological relations, which remain constant under topological transformations. …
View article
Topological Fundamental Groups and Small Generated Coverings Open
This paper is devoted to study some topological properties of the SG subgroup, π sg 1 (X, x), of the quasitopological fundamental group of a based space (X, x), π qtop 1 (X, x), its topological properties as a subgroup of the topological f…
View article
On uniformly recurrent motions of topological semigroup actions Open
Let G ↷ X be a topological action of a topological semigroup $G$ on a compact metric space $X$. We show in this paper that for any given point $x$ in $X$, the following two properties that both approximate to periodicity are equivalent to …
View article
(L,M)-fuzzy topological-convex spaces Open
In this paper, the notion of (L,M)-fuzzy topological-convex spaces is introduced and some of its characterizations are obtained. Then the notion of (L,M)-fuzzy convex enclosed relation spaces is introduced and its one-to-one correspondence…
View article
Dynamically characterizing topological phases by high-order topological charges Open
We propose a new theory to characterize equilibrium topological phase with\nnon-equilibrium quantum dynamics by introducing the concept of high-order\ntopological charges, with novel phenomena being predicted. Through a dimension\nreductio…
View article
Regularity of fuzzy convergence spaces Open
(Fuzzy) convergence spaces are extensions of (fuzzy) topological spaces. ⊤-convergence spaces are one of important fuzzy convergence spaces. In this paper, we present an extending dual Fischer diagonal condition, and making use of this we …
View article
Hereditary properties of semi-separation axioms and their applications Open
The paper studies the open-hereditary property of semi-separation axioms and applies it to the study of digital topological spaces such as an n-dimensional Khalimsky topological space, a Marcus-Wyse topological space and so on. More precis…
View article
Fans and their applications in General Topology, Functional Analysis and Topological Algebra Open
A family of closed subsets of a topological space $X$ is called a (strict) $Cld$-fan in $X$ if this family is (strictly) compact-finite but not locally finite in $X$. Applications of (strict) $Cld$-fans are based on a simple observation th…
View article
α-Topological Vector Spaces Open
The main objective of this paper is to present the study of α-topological vector spaces. α-topological vector spaces are defined by using α-open sets and α-irresolute mappings. Notions of convex, balanced and bounded set are introduced and…
View article
Categories of Open Sets in Generalized Primal Topological Spaces Open
In this research article, we define some categories of open sets over a generalized topological space given together with a primal collection. In addition, we clarify some of its characteristics and investigate the relationships between th…
View article
Limit Points and Separation Axioms with Respect to Supra Semi-open Sets Open
Sometimes we need to minimize the conditions of topology for different reasons such as obtaining more convenient structures to describe some real-life problems, or constructing some counterexamples whom show the interrelations between cert…
View article
Announcement as effort on topological spaces Open
We propose a multi-agent logic of knowledge, public and arbitrary announcements, that is interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort modali…
View article
On some spaces via topological ideals Open
Our main purpose is to introduce and investigate the concepts of some forms of spaces via topological ideals. Some characterizations of some forms of spaces via topological ideals are established. Moreover, several properties of ⋆ \star …
View article
Tree algebras over topological vector spaces in rough path theory Open
We work with non-planar rooted trees which have a label set given by an arbitrary vector space $V$. By equipping $V$ with a complete locally convex topology, we show how a natural topology is induced on the tree algebra over $V$. In this c…
View article
Order convergence in infinite-dimensional vector lattices is not topological Open
In this note, we show that the order convergence in a vector lattice $X$ is not topological unless $\dim X