scholarly journals The Absolutely Strongly Star-Hurewicz Property with Respect to an Ideal

2020 ◽  
Vol 76 (1) ◽  
pp. 81-94
Author(s):  
Sumit Singh ◽  
Brij K. Tyagi ◽  
Manoj Bhardwaj
Keyword(s):  
Dense Subset ◽  
Topological Properties ◽  
Hurewicz Property ◽  
The Relationship

AbstractAspace X is said to have the absolutely strongly star -𝒤-Hurewicz (ASS𝒤H) property if for each sequence (𝒰n : n ∈ 𝕅)of opencovers of X and each dense subset Y of X, there is a sequence (Fn : n ∈ 𝕅) of finite subsets of Y such that for each x ∈ X, {n ∈ 𝕅 : x ∉ St(Fn, 𝒰n)}∈ 𝒤, where 𝒤 is the proper admissible ideal of 𝕅. In this paper, we investigate the relationship between the ASS𝒤H property and other related properties and study the topological properties of the ASS𝒤H property. This paper generalizes several results of Song [25] to the larger class of spaces having the ASS𝒤H properties.

scholarly journals On weakly Hurewicz spaces

Filomat ◽  
2015 ◽  
Vol 29 (4) ◽  
pp. 667-671 ◽  
Author(s):  
Yan-Kui Song ◽  
Rui Li
Keyword(s):  
Dense Subset ◽  
Topological Properties ◽  
The Relationship

A space X is weakly Hurewicz if for each sequence (Un : n ? N) of open covers of X, there are a dense subset Y ? X and finite subfamilies Vn ? Un(n ? N) such that for every point of Y is contained in SVn for all but finitely many n. In this paper, we investigate the relationship between Hurewicz spaces and weakly Hurewicz spaces, and also study topological properties of weakly Hurewicz spaces.

On Star-K-I-Hurewicz Property

2021 ◽  
Vol 78 (1) ◽  
pp. 157-166
Author(s):  
Sumit Singh ◽  
Harsh V. S. Chauhan ◽  
Vikesh Kumar
Keyword(s):  
Topological Properties ◽  
Hurewicz Property ◽  
The Relationship ◽  
Compact Subsets

Abstract A space X is said to have the star-K-I-Hurewicz property (SKIH) [Tyagi, B. K.—Singh, S.—Bhardwaj, M. Ideal analogues of some variants of Hurewicz property, Filomat 33 (2019), no. 9, 2725–2734] if for each sequence (Un : n ∈ ℕ) of open covers of X there is a sequence (Kn : n ∈ ℕ) of compact subsets of X such that for each x ∈ X, {n ∈ ℕ : x ∉ St(Kn, Un )} ∈ I, where I is the proper admissible ideal of ℕ. In this paper, we continue to investigate the relationship between the SKIH property and other related properties and study the topological properties of the SKIH property.

scholarly journals Remarks on neighborhood star-Lindelöf spaces II

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 875-880
Author(s):  
Yan-Kui Song
Keyword(s):  
Open Cover ◽  
Countable Subset ◽  
Topological Properties ◽  
Pseudocompact Spaces ◽  
The Relationship

A space X is said to be neighborhood star-Lindel?f if for every open cover U of X there exists a countable subset A of X such that for every open O?A, X=St(O,U). In this paper, we continue to investigate the relationship between neighborhood star-Lindel?f spaces and related spaces, and study topological properties of neighborhood star-Lindel?f spaces in the classes of normal and pseudocompact spaces. .

scholarly journals On the Set Version of Selectively Star-CCC Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Ljubiša D. R. Kočinac ◽  
Sumit Singh
Keyword(s):  
Nonempty Subset ◽  
Topological Properties ◽  
Open Problems ◽  
The Relationship

A space X is said to be set selectively star-ccc if for each nonempty subset B of X , for each collection U of open sets in X such that B ¯ ⊂ ∪ U , and for each sequence A n : n ∈ ℕ of maximal cellular open families in X , there is a sequence A n : n ∈ ℕ such that, for each n ∈ ℕ , A n ∈ A n and B ⊂ St ∪ n ∈ ℕ A n , U . In this paper, we introduce set selectively star-ccc spaces and investigate the relationship between set selectively star-ccc and other related spaces. We also study the topological properties of set selectively star-ccc spaces. Some open problems are posed.

scholarly journals Winding number selection on merons by Gaussian curvature’s sign

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Ricardo Gabriel Elías ◽  
Nicolás Vidal-Silva ◽  
Vagson L. Carvalho-Santos
Keyword(s):  
Gaussian Curvature ◽  
Domain Walls ◽  
Curved Surfaces ◽  
Two Dimensional ◽  
Winding Number ◽  
Direct Relation ◽  
Topological Properties ◽  
The Core ◽  
Magnetic Surfaces ◽  
The Relationship

Abstract We study the relationship between the winding number of magnetic merons and the Gaussian curvature of two-dimensional magnetic surfaces. We show that positive (negative) Gaussian curvatures privilege merons with positive (negative) winding number. As in the case of unidimensional domain walls, we found that chirality is connected to the polarity of the core. Both effects allow to predict the topological properties of metastable states knowing the geometry of the surface. These features are related with the recently predicted Dzyaloshinskii-Moriya emergent term of curved surfaces. The presented results are at our knowledge the first ones drawing attention about a direct relation between geometric properties of the surfaces and the topology of the hosted solitons.

scholarly journals Application of Algorithmic Manifold to Exponential Time

2017 ◽  
Author(s):  
Takuya Yabu
Keyword(s):  
Turing Machine ◽  
Turing Machines ◽  
Topological Properties ◽  
Exponential Time ◽  
Polynomial Time Algorithms ◽  
Exponential Time Algorithms ◽  
Deterministic Turing Machine ◽  
The Relationship ◽  
Np Problem ◽  
Machine Problem

In the previous paper, I defined algorithmic manifolds simulating polynomial-time algorithms, and I showed topological properties for P problem and NP problem and that NP problem can be transformed into deterministic Turing machine problem.　In this paper, I define algorithmic manifolds simulating exponential-time algorithms and, I show topological properties for EXPTIME problem and NEXPTIME problem. I also discuss the relationship between NEXPTIME and deterministic Turing machines.

scholarly journals Bridge Graphs and Deodhar Parametrizations for Positroid Varieties

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Rachel Karpman
Keyword(s):  
Particle Physics ◽  
Dense Subset ◽  
Regular Map ◽  
Nous Montrons ◽  
Planar Network ◽  
International Audience ◽  
Nous Appellerons ◽  
Combinatorial Constructions ◽  
Obtient Alors ◽  
The Relationship

International audience A <i>parametrization</i> of a positroid variety $\Pi$ of dimension $d$ is a regular map $(\mathbb{C}^{\times})^{d} \rightarrow \Pi$ which is birational onto a dense subset of $\Pi$. There are several remarkable combinatorial constructions which yield parametrizations of positroid varieties. We investigate the relationship between two families of such parametrizations, and prove they are essentially the same. Our first family is defined in terms of Postnikov’s <i>boundary measurement map</i>, and the domain of each parametrization is the space of edge weights of a planar network. We focus on a special class of planar networks called <i>bridge graphs</i>, which have applications to particle physics. Our second family arises from Marsh and Rietsch’s parametrizations of Deodhar components of the flag variety, which are indexed by certain subexpressions of reduced words. Projecting to the Grassmannian gives a family of parametrizations for each positroid variety. We show that each Deodhar parametrization for a positroid variety corresponds to a bridge graph, while each parametrization from a bridge graph agrees with some projected Deodhar parametrization. Soit $\Pi$ une variété positroïde. Nous appellerons <i>paramétrisation</i> toute application régulière $(\mathbb{C}^{\times})^{d} \rightarrow \Pi$ qui est un isomorphisme birégulier sur un sous-ensemble dense de $\Pi$. On sait que plusieurs constructions combinatoires donnent des paramétrisations intéressantes. Le but du présent article est d’investiguer deux familles de telles paramétrisations et de montrer, essentiellement, qu’elles coïncident. La première famille trouve son origine dans la <i>fonction de mesure des bords</i> de Postnikov. Le domaine de chaque paramétrisation est en ce cas-ci l’ensemble de poids des arêtes d’un réseau planaire pondéré. Nous nous concentrons sur une classe particulière de réseaux planaires, les <i>graphes de ponts</i>, ayant des applications à la physique subatomique. La deuxième famille provient des paramétrisations de Marsh et de Rietsch des composantes de Deodhar (indexées par certaines sous-expressions de mots réduits de permutations) de la variété de drapeaux. On obtient alors des paramétrisations de cellules de positroïdes en appliquant la projection à la grassmannienne. Nous montrons que chaque paramétrisation de Deodhar correspond à un graphe de ponts; d’autre part, chaque paramétrisation provenant d’un graphe de ponts s’accorde avec quelque paramétrisation de Deodhar.

scholarly journals On star-K-Hurewicz spaces

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1279-1285 ◽  
Author(s):  
Yan-Kui Song
Keyword(s):  
Topological Properties ◽  
The Relationship ◽  
Compact Subsets

A space X is star-K-Hurewicz if for each sequence (Un : n ? N) of open covers of X there exists a sequence (Kn : n ? N) of compact subsets of X such that for each x ? X, x ? St(Kn,Un) for all but finitely many n. In this paper, we investigate the relationship between star-K-Hurewicz spaces and related spaces by giving some examples, and also study topological properties of star-K-Hurewicz spaces.

scholarly journals -openness of non-uniform hyperbolic diffeomorphisms with bounded -norm

2019 ◽  
Vol 40 (11) ◽  
pp. 3078-3104
Author(s):  
CHAO LIANG ◽  
KARINA MARIN ◽  
JIAGANG YANG
Keyword(s):  
Lyapunov Exponents ◽  
Dense Subset ◽  
Topological Properties ◽  
Hyperbolic Diffeomorphisms ◽  
Uniform Hyperbolicity ◽  
Partially Hyperbolic ◽  
The Stability ◽  
Bounded Norm ◽  
Volume Preserving

We study the $C^{1}$-topological properties of the subset of non-uniform hyperbolic diffeomorphisms in a certain class of $C^{2}$ partially hyperbolic symplectic systems which have bounded $C^{2}$ distance to the identity. In this set, we prove the stability of non-uniform hyperbolicity as a function of the diffeomorphism and the measure, and the existence of an open and dense subset of continuity points for the center Lyapunov exponents. These results are generalized to the volume-preserving context.

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