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Journal articles on the topic '2)*- -closed set'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Dr., C. Rajan. "ON (1, 2)*- - CLOSED SETS IN BITOPOLOGICAL SPACE." International Journal of Current Research and Modern Education, Special Issue (August 24, 2017): 148–55. https://doi.org/10.5281/zenodo.848255.

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In this paper, we offer a new class of sets called (1, 2)*--closed sets in bitopological spaces and we study some of its basic properties. It turns out that this class lies between the class of t<sub>1,2</sub>-closed sets and the class of (1, 2)*-g-closed sets.

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2

Reepa, Biswas, Asokan R., and Premkumar R. "Nano (1, 2)*-locally closed sets and its generalization in nano bitopological spaces." Asia Mathematika 8, no. 3 (2025): 35–41. https://doi.org/10.5281/zenodo.14794562.

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In this paper, we focused on the N(1, 2)*-LC set in nanobitopological spaces and certain properties of these investigated. Also, we studied the N(1, 2)*-GLC set, N(1, 2)*-GLC* set, and N(1, 2)*-GLC** set and established their various characteristic properties.

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3

Chen, Guantao, Hein van der Holst, Alexandr Kostochka, and Nana Li. "Extremal Union-Closed Set Families." Graphs and Combinatorics 35, no. 6 (2019): 1495–502. http://dx.doi.org/10.1007/s00373-019-02087-2.

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4

Ankit, Gupta. "On \(\pi gs-\lambda\) Closed Sets in Generalized Topological Spaces." Journal of Advanced Studies in Topology 13, no. 1-2 (2023): 7–13. https://doi.org/10.5281/zenodo.7905124.

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In this paper, a new class of generalized closed sets called \(\pi gs-\lambda\) closed sets are introduced and some of its properties are studied. Along with this, the notion of \(\pi gs-\lambda\)-continuity and \(\pi gs-\lambda\)-\(T(1/2)\) spaces are introduced.

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5

Yu, Tzu-Ling J., and Robert S. Schlauch. "Diagnostic Precision of Open-Set Versus Closed-Set Word Recognition Testing." Journal of Speech, Language, and Hearing Research 62, no. 6 (2019): 2035–47. http://dx.doi.org/10.1044/2019_jslhr-h-18-0317.

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Purpose The aim of the study was to examine the precision of forced-choice (closed-set) and open-ended (open-set) word recognition (WR) tasks for identifying a change in hearing. Method WR performance for closed-set (4 and 6 choices) and open-set tasks was obtained from 70 listeners with normal hearing. Speech recognition was degraded by presenting monosyllabic words in noise (−8, −4, 0, and 4 signal-to-noise ratios) or processed by a sine wave vocoder (2, 4, 6, and 8 channels). Results The 2 degraded speech understanding conditions yielded similarly shaped, monotonically increasing psychometr

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Ilyin, B. P., and V. I. Panteleev. "Lattice of $E$-closed Classes of Multifunctions of Rank 2." Bulletin of Irkutsk State University. Series Mathematics 48 (2024): 111–28. http://dx.doi.org/10.26516/1997-7670.2024.48.111.

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Multifunctions are discrete functions defined on a finite set and returning as their values all subsets of the considered set. The paper considers the classification of multifunctions defined on a two-element set with respect to the E-closure operator. E-closed sets of multifunctions are sets that are closed under superposition, the closure operator with branching by the equality predicate, the identification of variables, and the addition of dummy variables. The concept of separating sets was introduced using a greedy algorithm for the set covering problem, and 22 classes of separating sets w

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E., Kungumaraj, and Nirmaladevi K. "Fuzzy Strongly g s Closed sets in Fuzzy Topological spaces." International Journal of Trend in Scientific Research and Development 2, no. 2 (2018): 857–59. https://doi.org/10.31142/ijtsrd9482.

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In this paper, we have introduced and study the concept of strongly g s closed set in Fuzzy topological spaces and discuss some of its properties. E. Kungumaraj | K. Nirmaladevi "Fuzzy Strongly g*s Closed sets in Fuzzy Topological spaces" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-2 , February 2018, URL: https://www.ijtsrd.com/papers/ijtsrd9482.pdf

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8

Bhattacharya, Baby, Arnab Paul, and Sudip Debnath. "Some Properties of 1,2*-Locally Closed Sets." International Journal of Analysis 2014 (March 31, 2014): 1–5. http://dx.doi.org/10.1155/2014/393618.

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A new kind of generalization of (1, 2)*-closed set, namely, (1, 2)*-locally closed set, is introduced and using (1, 2)*-locally closed sets we study the concept of (1, 2)*-LC-continuity in bitopological space. Also we study (1, 2)*-contracontinuity and lastly investigate its relationship with (1, 2)*-LC-continuity.

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9

Al Ghour, Samer. "On Soft Generalized ω-Closed Sets and Soft T1/2 Spaces in Soft Topological Spaces". Axioms 11, № 5 (2022): 194. http://dx.doi.org/10.3390/axioms11050194.

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In this paper, we define a soft generalized ω-closed set, which is a generalization of both the soft ω-closed set and the soft generalized closed set. We show that the classes of generalized closed sets and generalized ω-closed sets coincide in soft anti-locally countable soft topological spaces. Additionally, in soft locally countable soft topological spaces, we show that every soft set is a soft generalized ω-closed set. Furthermore, we prove that the classes of soft generalized closed sets and soft generalized ω-closed sets coincide in the soft topological space (X,τω,A). In addition to the

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10

Shen, Jie, David Yoon, Huahao Shou, and Dong-Ming Zhao. "A Set of Denoising Algorithms for 2-D Closed Curves." Computer-Aided Design and Applications 3, no. 1-4 (2006): 1–10. http://dx.doi.org/10.1080/16864360.2006.10738436.

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11

Koh, K. M., and K. S. Poh. "Products of graphs with their closed-set lattices." Discrete Mathematics 69, no. 3 (1988): 241–51. http://dx.doi.org/10.1016/0012-365x(88)90053-2.

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12

Thomas, Morgan. "Approximating Cartesian Closed Categories in NF-Style Set Theories." Journal of Philosophical Logic 47, no. 1 (2017): 143–60. http://dx.doi.org/10.1007/s10992-017-9425-2.

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13

Sivak, Andrei G. "Each nowhere dense nonvoid closed set in Rn is a σ-limit set". Fundamenta Mathematicae 149, № 2 (1996): 183–90. http://dx.doi.org/10.4064/fm-149-2-183-190.

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14

Осіпчук, Тетяна. "On closed weakly m-convexsets." Proceedings of the International Geometry Center 15, no. 1 (2022): 50–65. http://dx.doi.org/10.15673/tmgc.v15i1.2139.

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In the present work we study properties of generally convex sets in the n-dimensional real Euclidean space Rn, (n>1), known as weakly m-convex, m=1,...,n-1. An open set of Rn is called weakly m-convex if, for any boundary point of the set, there exists an m-dimensional plane passing through this point and not intersecting the given set. A closed set of Rn is called weakly m-convex if it is approximated from the outside by a family of open weakly m-convex sets. A point of the complement of a set of Rn to the whole space is called an m-nonconvexity point of the set if any m-dimensional plane

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15

DUVAL, WHITNEY, JOHN SCHULTE, CHRISTOPHER SEATON, and BRADFORD TAYLOR. "CLASSIFYING CLOSED 2-ORBIFOLDS WITH EULER CHARACTERISTICS." Glasgow Mathematical Journal 52, no. 3 (2010): 555–74. http://dx.doi.org/10.1017/s001708951000042x.

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AbstractWe determine the extent to which the collection of Γ-Euler–Satake characteristics classify closed 2-orbifolds. In particular, we show that the closed, connected, effective, orientable 2-orbifolds are classified by the Γ-Euler–Satake characteristics corresponding to free or free abelian Γ and are not classified by those corresponding to any finite set of finitely generated discrete groups. These results demonstrate that the Γ-Euler–Satake characteristics corresponding to free abelian Γ constitute new invariants of orbifolds. Similarly, we show that such a classification is neither possi

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16

Adolfo, Niña Jeane, Imelda Aniversario, and Ferdinand Jamil. "Closed Geodetic Hop Domination in Graphs." European Journal of Pure and Applied Mathematics 17, no. 3 (2024): 1618–36. http://dx.doi.org/10.29020/nybg.ejpam.v17i3.5241.

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Let G be a simple, undirected and connected graph. A subset S ⊆ V (G) is a geodetic cover of G if IG[S] = V (G), where IG[S] is the set of all vertices of G lying on any geodesic between two vertices in S. A geodetic cover S of G is a closed geodetic cover if the vertices in S are sequentially selected as follows: Select a vertex v1 and let S1 = {v1}. If G is nontrivial, select a vertex v2 ̸= v1 and let S2 = {v1, v2}. Where possible, for i ≥ 3, successively select vertex vi ∈/ IG[Si−1] and let Si = {v1, v2, ..., vi}. Then there exists a positive integer k such that Sk = S. A geodetic cover S o

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17

Bhattacharyya, Anjana. "A STRONG FORM OF GENERALIZED CLOSED SET IN A FUZZY TOPOLOGICAL SPACE." South East Asian Journal of Mathematics and Mathematical Sciences 20, no. 02 (2024): 401–14. https://doi.org/10.56827/seajmms.2024.2002.28.

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In this paper a strong form of fuzzy generalized closed set, viz., $fg^{*}s$-closed set is introduced and studied. With the help of this newly defined set, a new type of idempotent operator is introduced. Using this operator as a basic tool, here we introduce and study $fg^{*}s$-open and $fg^{*}s$-closed functions the class of which are strictly larger than that of fuzzy open (resp, $fg$-open) and fuzzy closed (resp., $fg$-closed) functions respectively and weaker than that of $fg\delta$-open and $fg\delta$-closed functions respectively. In the last section we introduce $fg^{*}s$-$T_{2}$-space

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18

Lau, D., and M. Miyakawa. "CLASSIFICATION AND ENUMERATION OF BASES IN Pk(2)." Asian-European Journal of Mathematics 01, no. 02 (2008): 255–82. http://dx.doi.org/10.1142/s1793557108000242.

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Let k ≥ 2, Ek := {0, 1,…, k – 1}, and let Pk denote the set of all k-valued logical functions, i.e., of maps [Formula: see text] for n = 1, 2, … We denote by Pk(2) the set of all functions of Pk whose range contains no more than two elements. The set Pk(2) is a closed set (or class) with respect to the usual superposition operations and all maximal closed subsets of Pk(2) are known. For each f ∈ Pk(2) we determine its characteristic vectors with respect to the maximal classes and give an explicit formula for the total number of the characteristic vectors in terms of the numbers of the equivale

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19

Geschke, Stefan. "2-dimensional Convexity Numbers and P4-free Graphs." Canadian Mathematical Bulletin 57, no. 1 (2014): 61–71. http://dx.doi.org/10.4153/cmb-2012-031-5.

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AbstractFor S ⊆ ℝn a set C ⊆ S is an m-clique if the convex hull of no m-element subset of C is contained in S. We show that there is essentially just one way to construct a closed set S ⊆ ℝ2 without an uncountable 3-clique that is not the union of countably many convex sets. In particular, all such sets have the same convexity number; that is, they require the same number of convex subsets to cover them. The main result follows from an analysis of the convex structure of closed sets in ℝ2 without uncountable 3-cliques in terms of clopen, P4-free graphs on Polish spaces.

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20

Selvi, G., and I. Rajasekaran. "ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES." Advances in Mathematics: Scientific Journal 9, no. 11 (2020): 9353–60. http://dx.doi.org/10.37418/amsj.9.11.41.

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This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

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21

Koh, K. M., and K. S. Poh. "On the uniformity of the closed-set lattice of a tree." Discrete Mathematics 61, no. 1 (1986): 61–70. http://dx.doi.org/10.1016/0012-365x(86)90028-2.

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22

Howland, Michael F., Aditya S. Ghate, Jesús Bas Quesada, et al. "Optimal closed-loop wake steering – Part 2: Diurnal cycle atmospheric boundary layer conditions." Wind Energy Science 7, no. 1 (2022): 345–65. http://dx.doi.org/10.5194/wes-7-345-2022.

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Abstract. The magnitude of wake interactions between individual wind turbines depends on the atmospheric stability. We investigate strategies for wake loss mitigation through the use of closed-loop wake steering using large eddy simulations of the diurnal cycle, in which variations in the surface heat flux in time modify the atmospheric stability, wind speed and direction, shear, turbulence, and other atmospheric boundary layer (ABL) flow features. The closed-loop wake steering control methodology developed in Part 1 (Howland et al., 2020c, https://doi.org/10.5194/wes-5-1315-2020) is implement

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23

Dalia raad abd and Gazwan Haider Abdulhusein. "Fuzzy Nano -Generalized Closed Set in Fuzzy Nano Symmetric Topology." Mustansiriyah Journal of Pure and Applied Sciences 3, no. 2 (2025): 169–77. https://doi.org/10.47831/mjpas.v3i2.353.

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In this paper we introduced new types of fuzzy nanoopen sets, called fuzzy nanoopen sets, and studied some properties of fuzzy nanogeneralized closed sets in fuzzy nanosymmetric topology. Also, we studied some separation axioms, called FNζ-T0S, FNζ-T_(1/2)S, and FNζ-T1S, and we studied the relationship between them under the condition of fuzzy nanosymmetric topology and proofed the converse relations, which were studied for the first time, and obtained several important properties.

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24

Lebl, Jiří. "Segre-degenerate points form a semianalytic set." Proceedings of the American Mathematical Society, Series B 9, no. 16 (2022): 159–73. http://dx.doi.org/10.1090/bproc/99.

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We prove that the set of Segre-degenerate points of a real-analytic subvariety X X in C n {\mathbb {C}}^n is a closed semianalytic set. It is a subvariety if X X is coherent. More precisely, the set of points where the germ of the Segre variety is of dimension k k or greater is a closed semianalytic set in general, and for a coherent X X , it is a real-analytic subvariety of X X . For a hypersurface X X in C n {\mathbb {C}}^n , the set of Segre-degenerate points, X [ n ] X_{[n]} , is a semianalytic set of dimension at most 2 n − 4 2n-4 . If X X is coherent, then X [ n ] X_{[n]} is a complex su

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25

HIMEKI, YUTARO, and YUTAKA ISHII. "is regular-closed." Ergodic Theory and Dynamical Systems 40, no. 1 (2018): 213–20. http://dx.doi.org/10.1017/etds.2018.27.

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For each $n\geq 2$, we investigate a family of iterated function systems which is parameterized by a common contraction ratio $s\in \mathbb{D}^{\times }\equiv \{s\in \mathbb{C}:0<|s|<1\}$ and possesses a rotational symmetry of order $n$. Let ${\mathcal{M}}_{n}$ be the locus of contraction ratio $s$ for which the corresponding self-similar set is connected. The purpose of this paper is to show that ${\mathcal{M}}_{n}$ is regular-closed, that is, $\overline{\text{int}\,{\mathcal{M}}_{n}}={\mathcal{M}}_{n}$ holds for $n\geq 4$. This gives a new result for $n=4$ and a simple geometric proof

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26

Munther Hassan, Marwah, and Ali Al-Hachami. "On Semi pre-generalized-closed sets." Wasit Journal of Pure sciences 1, no. 2 (2022): 71–86. http://dx.doi.org/10.31185/wjps.39.

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In this paper, a new class of called semi-pre-generalised closed set in topological space are introduced and studied. Also some of their properties have been investigated. We also introduce sp-T1/2 space, and studied the relationship between spg-closedset and some space in topological space, as well discuss some properties, theorem, corollary and examples.

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27

Podolko, D. K. "On one continual set of в-closed classes of the multivalued logic functions". Prikladnaya diskretnaya matematika, № 24 (1 червня 2014): 12–20. http://dx.doi.org/10.17223/20710410/24/2.

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28

Hidalgo, Rubén A., and Gustavo Labbé. "Fixed points parameters for Teichmüller space of closed Riemann surfaces." Proyecciones (Antofagasta) 19, no. 1 (2017): 65–94. https://doi.org/10.22199/s0716-09172000000100006.

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In this note we provide a set of parameters for the Teichmüller space, of genus g ? 2, given by fixed points of some special set of generators for the uniformizing Fuchsian groups. Explicit computations are given in low genus.

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29

Osipchuk, Tetiana. "Topological properties of closed weakly m-semiconvex sets." Ukrainian Mathematical Bulletin 18, no. 4 (2021): 540–59. http://dx.doi.org/10.37069/1810-3200-2021-18-4-6.

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The present work considers properties of generally convex sets in the $n$-dimensional real Euclidean space $\mathbb{R}^{n}$, $n>1$, known as weakly $m $-semiconvex, $m=1,2,\ldots ,n-1$. For all that, the subclass of not $m$-semiconvex sets is distinguished from the class of weakly $m$-semiconvex sets. A set of the space $\mathbb{R}^{n}$ is called \textbf{\emph{$m$-semiconvex}} if, for any point of the complement of the set to the whole space, there is an $m$-dimensional half-plane passing through this point and not intersecting the set. An open set of $\mathbb{R}^{n}$ is called weakly $m$-s

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LECHTENFELD, OLAF, and ALEXANDER D. POPOV. "CLOSED N=2 STRINGS: PICTURE-CHANGING, HIDDEN SYMMETRIES AND SDG HIERARCHY." International Journal of Modern Physics A 15, no. 26 (2000): 4191–236. http://dx.doi.org/10.1142/s0217751x00001865.

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We study the action of picture-changing and spectral flow operators on a ground ring of ghost number zero operators in the chiral BRST cohomology of the closed N=2 string and describe an infinite set of symmetry charges acting on physical states. The transformations of physical string states are compared with symmetries of self-dual gravity which is the effective field theory of the closed N=2 string. We derive all infinitesimal symmetries of the self-dual gravity equations in (2+2)-dimensional space–time and introduce an infinite hierarchy of commuting flows on the moduli space of self-dual m

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Medvedev, V., and E. Zhuzhoma. "Any closed 3-manifold supports A-flows with 2-dimensional expanding attractors." Applied Mathematics and Nonlinear Sciences 5, no. 2 (2020): 307–10. http://dx.doi.org/10.2478/amns.2020.2.00053.

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AbstractWe prove that given any closed 3-manifold M3, there is an A-flow ft on M3 such that the non-wandering set NW (ft) consists of 2-dimensional non-orientable expanding attractor and trivial basic sets.

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32

Panteleev, V. I., and E. S. Taglasov. "On the Lattice of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><msub><mi>S</mi><mi>I</mi></msub></math>-closed Classes of Multifunctions on Two-elements Set." Bulletin of Irkutsk State University. Series Mathematics 38 (2021): 96–111. http://dx.doi.org/10.26516/1997-7670.2021.38.96.

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The paper considers multifunctions on a two-element set with superposition and the equality predicate branching operator. The superposition operator is based on the intersection of sets. The main purpose of the work is to describe all closed classes with respect to the considered operators. The equality predicate branching operator allows the task to be reduced to a description of all closed classes generated by 2-variable multifunctions. Using this, it is shown that the lattice of classes closed with respect to the considered operators contains 237 elements. A generating set is specified for

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33

Malev, Sergey. "The images of non-commutative polynomials evaluated on 2 × 2 matrices over an arbitrary field." Journal of Algebra and Its Applications 13, no. 06 (2014): 1450004. http://dx.doi.org/10.1142/s0219498814500042.

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Let p be a multilinear polynomial in several non-commuting variables with coefficients in an arbitrary field K. Kaplansky conjectured that for any n, the image of p evaluated on the set Mn(K) of n × n matrices is either zero, or the set of scalar matrices, or the set sl n(K) of matrices of trace 0, or all of Mn(K). This conjecture was proved for n = 2 when K is closed under quadratic extensions. In this paper, the conjecture is verified for K = ℝ and n = 2, also for semi-homogeneous polynomials p, with a partial solution for an arbitrary field K.

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34

Abdollahi, Alireza, and Majid Arezoomand. "Finite nilpotent groups that coincide with their 2-closures in all of their faithful permutation representations." Journal of Algebra and Its Applications 17, no. 04 (2018): 1850065. http://dx.doi.org/10.1142/s0219498818500652.

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Let [Formula: see text] be any group and [Formula: see text] be a subgroup of [Formula: see text] for some set [Formula: see text]. The [Formula: see text]-closure of [Formula: see text] on [Formula: see text], denoted by [Formula: see text], is by definition, [Formula: see text] The group [Formula: see text] is called [Formula: see text]-closed on [Formula: see text] if [Formula: see text]. We say that a group [Formula: see text] is a totally[Formula: see text]-closed group if [Formula: see text] for any set [Formula: see text] such that [Formula: see text]. Here we show that the center of an

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35

Ivanov, Alexander A. "Closed Majorana representations of {3, 4}⁺-transposition groups." Advances in Geometry 22, no. 4 (2022): 487–94. http://dx.doi.org/10.1515/advgeom-2022-0015.

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Abstract The paper contributes to Majorana theory. Among the eight non-trivial Norton–Sakuma algebras, four algebras are closed on the set of Majorana generators. These algebras are 2A, 2B, 3C and 4B. The classification of Majorana representations restricted to the closed shapes was anticipated for a long time. In the present article the classification is achieved for shapes restricted to 2A, 3C and 4B and for the set of generating involutions in the target group forming a single conjugacy class. Timmesfeld’s classification of {3, 4}+-transposition groups reduces to consideration of just three

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36

Kruglikov, B. S. "The image inH 2(Q 3;ℝ) of the set of closed 2-forms with preassigned kernel". Journal of Mathematical Sciences 94, № 2 (1999): 1218–25. http://dx.doi.org/10.1007/bf02364877.

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37

van den Dries, Lou, David Marker, and Gary Martin. "Definable equivalence relations on algebraically closed fields." Journal of Symbolic Logic 54, no. 3 (1989): 928–35. http://dx.doi.org/10.2307/2274753.

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This article was inspired by the question: is there a definable equivalence relation on the field of complex numbers, each of whose equivalence classes has exactly two elements? The answer turned out to be no, as we now explain in greater detail.Let Κ be an algebraically closed field and let E be a definable equivalence relation on Κ. [Note: By “definable” we will always mean “definable with parameters”.] Either E has one cofinite class, or all classes are finite and there is a number d such that all but a finite set of classes have cardinality d. In the latter case let B be the finite set of

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38

Hennigan, Robert F., Jonathan S. Fletcher, Steven Guard, and Nancy Ratner. "Proximity biotinylation identifies a set of conformation-specific interactions between Merlin and cell junction proteins." Science Signaling 12, no. 578 (2019): eaau8749. http://dx.doi.org/10.1126/scisignal.aau8749.

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Neurofibromatosis type 2 is an inherited, neoplastic disease associated with schwannomas, meningiomas, and ependymomas and that is caused by inactivation of the tumor suppressor gene NF2. The NF2 gene product, Merlin, has no intrinsic catalytic activity; its tumor suppressor function is mediated through the proteins with which it interacts. We used proximity biotinylation followed by mass spectrometry and direct binding assays to identify proteins that associated with wild-type and various mutant forms of Merlin in immortalized Schwann cells. We defined a set of 52 proteins in close proximity

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Hamja, Jamil, Imelda S. Aniversario, and Helen M. Rara. "On Weakly Connected Closed Geodetic Domination in Graphs Under Some Binary Operations." European Journal of Pure and Applied Mathematics 15, no. 2 (2022): 736–52. http://dx.doi.org/10.29020/nybg.ejpam.v15i2.4356.

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Let G be a simple connected graph. For S ⊆ V (G), the weakly connected closed geodetic dominating set S of G is a geodetic closure IG[S] which is between S and is the set of all vertices on geodesics (shortest path) between two vertices of S. We select vertices of Gsequentially as follows: Select a vertex v1 and let S1 = {v1}. Select a vertex v2 ̸= v1 and let S2 = {v1, v2}. Then successively select vertex vi ∈/ IG[Si−1] and let Si = {v1, v2, ..., vi} for i = 1, 2, ..., k until we select a vertex vk in the given manner that yields IG[Sk] = V (G). Also, the subgraph weakly induced ⟨S⟩w by S is c

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Mandal, Manasi, та Mandobi Banerjee. "Inscription on statistical convergence of order α". Filomat 35, № 7 (2021): 2341–47. http://dx.doi.org/10.2298/fil2107341m.

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In this article we recall a remarkable result stated as "For a fixed ?, 0 < ? ? 1, the set of all bounded statistically convergent sequences of order ? is a closed linear subspace of m (m is the set of all bounded real sequences endowed with the sup norm)" by Bhunia et al. (Acta Math. Hungar. 130 (1-2) (2012), 153-161) and to develop the objective of this perception we demonstrate that the set of all bounded statistically convergent sequences of order ? may not form a closed subspace in other sequence spaces. Also we determine two different sequence spaces in which the set of all statistica

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Lu, Xing Yang. "Example of minimizer of the average-distance problem with non closed set of corners." Rendiconti del Seminario Matematico della Università di Padova 137 (2017): 19–55. http://dx.doi.org/10.4171/rsmup/137-2.

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Dougherty, Randall. "Monotone but not positive subsets of the Cantor space." Journal of Symbolic Logic 52, no. 3 (1987): 817–18. http://dx.doi.org/10.1017/s0022481200029790.

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A subset of the Cantor space ω2 is called monotone iff it is closed upward under the partial ordering ≤ defined by x ≤ y iff x(n) ≤ y(n) for all n ∈ ω. A set is -positive (-positive) iff it is monotone and -positive set is a countable union of -positive sets; a -positive set is a countable intersection of -positive sets. (See Cenzer [2] for background information on these concepts.) It is clear that any -positive set is and monotone; the converse holds for n ≤ 2 [2] and was conjectured by Dyck to hold for greater n. In this note, we will disprove this conjecture by giving examples of monotone

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HOSSAIN, NESAR. "ROUGH I-CONVERGENCE OF SEQUENCES IN 2-NORMED SPACES." Journal of Inequalities and Special Functions 14, no. 3 (2023): 17–25. https://doi.org/10.54379/jiasf-2023-3-3.

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In this paper, we have introduced the notions of rough I-convergence of sequences and defined I-cluster point of a sequence and proved some results associated with this notion in 2-normed spaces. Also, we have defined rough I-limit set of a sequence and shown that this set is closed and convex. Further, we have defined the notion of rough I-Cauchy sequence in the same space.

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Boyd, Suzanne, Juan L. G. Guirao, and Michael Hero. "On Diffeomorphisms of Compact 2-Manifolds with All Nonwandering Points Being Periodic." International Journal of Bifurcation and Chaos 25, no. 14 (2015): 1540020. http://dx.doi.org/10.1142/s0218127415400209.

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The aim of the present paper is to study conditions under which all the nonwandering points are periodic points, for a discrete dynamical system of two variables defined on a compact manifold. We include a survey of known results in all dimensions, and study the remaining open question in dimension two. We present two results, one negative and one positive. The negative result: we construct a Kupka–Smale diffeomorphism in [Formula: see text] (which can be extended to a diffeomorphism of the sphere) with a closed set of periodic points that differs from the set of nonwandering points. The posit

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Neary, W. J., V. F. Hillier, T. Flute, D. Stephens, R. T. Ramsden, and D. G. R. Evans. "Use of a closed set questionnaire to measure primary and secondary effects of neurofibromatosis type 2." Journal of Laryngology & Otology 124, no. 7 (2010): 720–28. http://dx.doi.org/10.1017/s0022215110000460.

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AbstractObjectives:To identify the greatest difficulties reported by people affected by neurofibromatosis type 2, and to determine the relationship between the primary and secondary effects of the disease.Design:Postal questionnaire study.Setting:Questionnaire sent to subjects' home addresses.Participants:Eighty-seven adult patients under the care of the Manchester multidisciplinary neurofibromatosis type 2 team were invited to take part.Main outcome measure:The response rate was 62 out of 87 (71 per cent).Results:Respondents' answers emphasised that their greatest problem was deafness, which

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Norton, R. M., and D. G. Sarvate. "A note of the union-closed sets conjecture." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 55, no. 3 (1993): 411–13. http://dx.doi.org/10.1017/s1446788700034133.

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AbstractLet = {A1, …, An} be a union-closed set. This note establishes a property which must be possessed by any smallest counterexample to the Union-Closed Sets Conjecture. Specifically, a counterexample to the conjecture with minimal n has at least three distinct elements, each of which appears in exactly (n − 1)/2 of the .

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Grines, V. Z., and E. V. Zhuzhoma. "Cantor Type Basic Sets of Surface $A$-endomorphisms." Nelineinaya Dinamika 17, no. 3 (2021): 335–45. http://dx.doi.org/10.20537/nd210307.

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The paper is devoted to an investigation of the genus of an orientable closed surface $M^{2}$ which admits $A$-endomorphisms whose nonwandering set contains a one-dimensional strictly invariant contracting repeller $\Lambda_{r}$ with a uniquely defined unstable bundle and with an admissible boundary of finite type. First, we prove that, if $M^{2}$ is a torus or a sphere, then $M^{2}$ admits such an endomorphism. We also show that, if $\Omega$ is a basic set with a uniquely defined unstable bundle of the endomorphism $f\colon M^{2}\to M^{2}$ of a closed orientable surface $M^{2}$ and $f$ is not

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P., Padma. "( τi , τj ) * - Q* g closed sets in Bitopological spaces". Journal of Progressive Research in Mathematics 2, № 1 (2015): 69–79. https://doi.org/10.5281/zenodo.3980807.

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The aim of this paper is to introduced the new type of closed sets called ( τ<sub>i</sub> , τ<sub>j</sub> )* - Q* g closed set . We introduce and study a new class of spaces namely (τ<sub>i</sub> , τ<sub>j</sub> )* - Q*g T1/2 space and ( τ<sub>i</sub> , τ<sub>j</sub> )* - Q* g T3/4 space . Also we find some basic properties and applications of ( τ<sub>i</sub> , τ<sub>j</sub> )* - Q* g closed sets .

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AXON, LOGAN M. "MARTIN-LÖF RANDOMNESS IN SPACES OF CLOSED SETS." Journal of Symbolic Logic 80, no. 2 (2015): 359–83. http://dx.doi.org/10.1017/jsl.2014.76.

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AbstractAlgorithmic randomness was originally defined for Cantor space with the fair-coin measure. Recent work has examined algorithmic randomness in new contexts, in particular closed subsets of 2ɷ ([2] and [8]). In this paper we use the probability theory of closed set-valued random variables (RACS) to extend the definition of Martin-Löf randomness to spaces of closed subsets of locally compact, Hausdorff, second countable topological spaces. This allows for the study of Martin-Löf randomness in many new spaces, but also gives a new perspective on Martin-Löf randomness for 2ɷ and on the algo

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Govindaraj, Shrenik, and Sridar Govindaraj. "Closed circuit system in laparoscopy: SARS-CoV-2 pandemic." International Surgery Journal 7, no. 11 (2020): 3594. http://dx.doi.org/10.18203/2349-2902.isj20204424.

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Background: There is a big concern regarding transmission of Severe acute respiratory syndrome corona virus 2 (SARS-CoV-2) during laparoscopy and using energy devices through the carbon dioxide (CO2) pneumoperitoneum. So, we decided to use a novel indigenous innovative closed-circuit system (CCS) to avoid this contamination in operation theatre.Methods: We set out to do a prospective study in the safety of this innovative closed-circuit system in elective surgeries over 3 consecutive months of May to July 2020, during the peak of SARS-CoV-2 pandemic in a tertiary teaching hospital. We recruite

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