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Journal articles on the topic 'G - sets'

Author: Grafiati
Published: 5 June 2025
Last updated: 25 June 2025

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1

Lizasoain, I., and G. Ochoa. "Projective G-sets." Journal of Pure and Applied Algebra 126, no. 1-3 (1998): 287–96. http://dx.doi.org/10.1016/s0022-4049(96)00138-7.

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2

O., Nethaji, and Premkumar R. "Locally closed sets and g-locally closed sets in binary topological spaces." Asia Mathematika 7, no. 2 (2023): 21——26. https://doi.org/10.5281/zenodo.8368982.

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In this paper, we focused on locally closed sets in binary topological spaces and certain properties of these investigated. Also, we studied the binary generalized locally closed sets,  binary g-lc*, binary g-lc** and established their various characteristic properties.
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3

Hamant, Kumar Hamant. "On Q*g-closed sets." EPRA International Journal of Research and Development (IJRD) 9, no. 7 (2025): 189–90. https://doi.org/10.5281/zenodo.14872515.

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The author introduce the notion of Q*g-closed sets in the paper entitled Q*g-closed sets in topological space by P. Padma and S. Uday Kumar. However, there is a false theorem, namely Theorem 3.4. The correct statement of Theorem 3.4 is mentioned in this paper with correct proof and gave a counter-example in support of this theorem.
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4

Vijayalakshmi, S., and T. Indira. "?_1 ?_2-g ?-Closed sets in Bitopological Spaces." International Journal of Scientific Engineering and Research 5, no. 5 (2017): 83–86. https://doi.org/10.70729/2051701.

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5

HARANT, JOCHEN, ANJA PRUCHNEWSKI, and MARGIT VOIGT. "On Dominating Sets and Independent Sets of Graphs." Combinatorics, Probability and Computing 8, no. 6 (1999): 547–53. http://dx.doi.org/10.1017/s0963548399004034.

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For a graph G on vertex set V = {1, …, n} let k = (k1, …, kn) be an integral vector such that 1 [les ] ki [les ] di for i ∈ V, where di is the degree of the vertex i in G. A k-dominating set is a set Dk ⊆ V such that every vertex i ∈ V[setmn ]Dk has at least ki neighbours in Dk. The k-domination number γk(G) of G is the cardinality of a smallest k-dominating set of G.For k1 = · · · = kn = 1, k-domination corresponds to the usual concept of domination. Our approach yields an improvement of an upper bound for the domination number found by N. Alon and J. H. Spencer.If ki = di for i = 1, …, n, then the notion of k-dominating set corresponds to the complement of an independent set. A function fk(p) is defined, and it will be proved that γk(G) = min fk(p), where the minimum is taken over the n-dimensional cube Cn = {p = (p1, …, pn) [mid ] pi ∈ ℝ, 0 [les ] pi [les ] 1, i = 1, …, n}. An [Oscr ](Δ22Δn-algorithm is presented, where Δ is the maximum degree of G, with INPUT: p ∈ Cn and OUTPUT: a k-dominating set Dk of G with [mid ]Dk[mid ][les ]fk(p).
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6

Atkinswestley, A., and S. Chandrasekar. "NEUTROSOPHIC WEAKLY G*-CLOSED SETS." Advances in Mathematics: Scientific Journal 9, no. 5 (2020): 2853–61. http://dx.doi.org/10.37418/amsj.9.5.47.

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7

Attila, Nagy. "On congruence permutable $G$-sets." Commentationes Mathematicae Universitatis Carolinae 61, no. 2 (2020): 139–45. http://dx.doi.org/10.14712/1213-7243.2020.019.

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8

Peralta, J., and B. Torrecillas. "Graded codes by G-sets." ACM SIGSAM Bulletin 33, no. 3 (1999): 18. http://dx.doi.org/10.1145/347127.347316.

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9

Blass, Andreas. "On exponentiation of G-sets." Discrete Mathematics 135, no. 1-3 (1994): 69–79. http://dx.doi.org/10.1016/0012-365x(93)e0109-h.

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10

Parzanchevski, Ori. "On G-sets and isospectrality." Annales de l’institut Fourier 63, no. 6 (2013): 2307–29. http://dx.doi.org/10.5802/aif.2831.

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11

Baker, C. W. "On g*m-closed sets." International Journal of Contemporary Mathematical Sciences 9 (2014): 507–14. http://dx.doi.org/10.12988/ijcms.2014.4780.

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12

Amir, Assari, and Kasiri Hossein. "ON MEASURE TRANSITIVE G-SETS." JP Journal of Algebra, Number Theory and Applications 40, no. 5 (2018): 823–31. http://dx.doi.org/10.17654/nt040050823.

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13

Kannan, K., and D. Rajalakshmi. "Soft g-Locally Closed Sets." National Academy Science Letters 38, no. 3 (2015): 239–41. http://dx.doi.org/10.1007/s40009-014-0326-4.

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14

Uc, Mehmet, and Mustafa Alkan. "On Modules over G-sets." Journal of Mathematics and Statistics Studies 4, no. 4 (2023): 47–55. http://dx.doi.org/10.32996/jmss.2023.4.4.5.

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Let R be a commutative ring with unity, M a module over R and let S be a G–set for a finite group G. We define a set MS to be the set of elements expressed as the formal finite sum of the form ∑s∈Smss where ms∈M. The set MS is a module over the group ring RG under the addition and the scalar multiplication similar to the RG–module MG. With this notion, we not only generalize but also unify the theories of both of the group algebra and the group module, and we also establish some significant properties of (MS)RG. In particular, we describe a method for decomposing a given RG–module MS as a direct sum of RG–submodules. Furthermore, we prove the semisimplicity problem of (MS)RG with regard to the properties of MR, S and G.
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15

AL-Jarrah, Heyam H., Amani Rawshdeh, Khalid Y. Al-Zoubi, and Shefa A. Bani Melhem. "On $g \mu$-Paracompact Sets." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 5899. https://doi.org/10.29020/nybg.ejpam.v18i2.5899.

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In this work, we use the notion of the $g \mu$-paracompact space \cite{ADeb} to introduce two types of $g \mu$-paracompact sets called $\alpha$-$g \mu$-paracompact and $\beta$-$g \mu$-paracompact. We show that every $\alpha$-$g \mu$-paracompact set is $\beta$-$g \mu$-paracompact and if a generalized topological space $(S,\mu)$ is $g \mu$-paracompact, then every $\mu$-closed subset in $(S,\mu)$ is $\alpha$-$g \mu$-paracompact while every $\mu g$-closed subset in $(S, \mu)$ is $\beta$-$g \mu$-paracompact. Finally, we introduce the notion of $co$-$\alpha$-$g\mu$-paracompact set as an application of $\alpha$-$g\mu$-paracompact and study some of its features.
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16

Durga, N., R. Raja, and P. Thangavelu. "Approximations of Rough Sets via Filter by using g-increasing and g-decreasing Sets." International Journal of Computer Applications 161, no. 8 (2017): 23–30. http://dx.doi.org/10.5120/ijca2017913246.

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17

itra, V. Ch, та A. V. Vis hnu. "G-Nαg Closed Sets and G-Ngα Closed Sets in Grill Nano Topological Spaces". International Journal of Mathematics Trends and Technology 62, № 1 (2018): 20–26. http://dx.doi.org/10.14445/22315373/ijmtt-v62p505.

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18

Rajakumar, S., A. Vadivel, and K. Vairamanickam. "Minimal \(\tau^*\)-\(g\)-Open Sets and Maximal \(\tau^*\)-\(g\)-Closed Sets in Topological Spaces." Journal of Advanced Studies in Topology 3, no. 3 (2012): 48. http://dx.doi.org/10.20454/jast.2012.195.

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19

Hamant, Kumar Hamant. "On beeta*g-closed sets and beeta*-normal spaces." Acta Ciencia Indica XLI M, no. 1 (2025): 67–72. https://doi.org/10.5281/zenodo.14866811.

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In this paper, we introduce the notion of beeta*g-closed sets and we show that the family of all beeta*g-open sets in a topological spaces (X, T) is a topology for X which is finer than T. Further we obtain some characterizations and preservation theorems for beeta*-normality and normality. 
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20

V., Gopalakrishnan*1 M. Murugalingam2 &. R. Mariappan3. "ON πµ∗g-CLOSED SETS IN IDEAL GENERALIZED TOPOLOGICAL SPACES". GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 5, № 11 (2018): 348–52. https://doi.org/10.5281/zenodo.1624669.

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We  introduce  the  notions  of  πµ∗ g-closed  sets  by  using  the  notion of  µ-pre-I-open sets.  Further, we study the concept of πµ∗ g-closed sets and their relationships in an ideal generalized topological spaces by using these new notions.   2000 Mathematics Subject Classification: 54 A 05.  
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21

Journal, Baghdad Science. "ON G-OPEN SET." Baghdad Science Journal 4, no. 3 (2007): 482–84. http://dx.doi.org/10.21123/bsj.4.3.482-484.

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A new class of generalized open sets in a topological space, called G-open sets, is introduced and studied. This class contains all semi-open, preopen, b-open and semi-preopen sets. It is proved that the topology generated by G-open sets contains the topology generated by preopen,b-open and semi-preopen sets respectively.
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22

Ülger, A. "Characterizations of Riesz sets." MATHEMATICA SCANDINAVICA 108, no. 2 (2011): 264. http://dx.doi.org/10.7146/math.scand.a-15171.

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Let $G$ be a compact abelian group, $M(G)$ its measure algebra and $L^{1}(G)$ its group algebra. For a subset $E$ of the dual group $\widehat{G}$, let $M_{E}(G)=\{\mu\in M(G):\widehat{\mu}=0$ on $\widehat{G} \backslash E\}$ and $L_{E}^{1}(G)=\{a\in L^{1}(G):\widehat{a}=0$ on $\widehat{G}\backslash E\}$. The set $E$ is said to be a Riesz set if $M_{E}(G)=L_{E}^{1}(G)$. In this paper we present several characterizations of the Riesz sets in terms of Arens multiplication and in terms of the properties of the Gelfand transform $\Gamma :L_{E}^{1}(G)\rightarrow c_{0}(E)$.
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23

Abbott, H. L. "Sidon Sets." Canadian Mathematical Bulletin 33, no. 3 (1990): 335–41. http://dx.doi.org/10.4153/cmb-1990-056-6.

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AbstractDenote by g(n) the largest integer m such that every set of integers of size n contains a subset of size m whose pairwise sums are distinct. It is shown that g(n) > cn1/2 for any constant c < 2/25 and all sufficiently large n.
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24

G.Helen, Rajapushpam, Sivagami P., and Hari Siva Annam G. "mu I g-Dense sets and mu I g- Baire spaces in GITS." Asia Mathematika 5, no. 1 (2021): 158–67. https://doi.org/10.5281/zenodo.4734085.

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Our aim is to bring the idea of \(\mu_I~g\)-DGITS, \(\mu_I~g\)-NDGITS, \(\mu_I~g\)-CDGITS and \(\mu_I~g\)-Baire space on \(\mu_I~g\)-closed sets in GITS and some of the basic properties are to be discussed.
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25

Ahn, Seung-Ho, and Dae Heui Park. "G-CW COMPLEX STRUCTURES OF PROPER SEMIALGEBRAIC G-SETS." Honam Mathematical Journal 39, no. 1 (2017): 101–13. http://dx.doi.org/10.5831/hmj.2017.39.1.101.

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26

López, John J., H. Mauricio Ruiz, and Carlos A. Trujillo. "g-SIDON MODULAR SETS AND g-GOLOMB MODULAR RULERS." JP Journal of Algebra, Number Theory and Applications 39, no. 4 (2017): 401–15. http://dx.doi.org/10.17654/nt039040401.

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27

Caicedo, Yadira, Jhonny C. Gómez, and Carlos A. Trujillo. "B_{h}[g] MODULAR SETS FROM B_{h} MODULAR SETS." JP Journal of Algebra, Number Theory and Applications 37, no. 1 (2015): 1–19. http://dx.doi.org/10.17654/jpantaaug2015_001_019.

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28

R., Dr Ravikumar. "Soft s∗∗g-Locally Closed Sets." International Journal of Innovative Research in Information Security 10, no. 03 (2024): 228–37. http://dx.doi.org/10.26562/ijiris.2024.v1003.21.

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In the present paper, we continue the study of soft semi star generalized closed sets in soft topological spaces by introducing new concepts, namely soft s∗∗g-locally closed sets, soft s∗∗g-locally closed∗ sets, soft s∗∗g-locally closed∗∗ sets.
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29

Schneider, Carsten, and Claudius Wagemann. "Fuzzy sets are sets- a reply to Goertz and Mahoney." Qualitative & Multi-Method Research 11, no. 1 (2013): 20–23. https://doi.org/10.5281/zenodo.911094.

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As stated in our first comments, we share G&M’s vision of qualitative research as being rooted in set theory. Precisely because we think that this is a plausible proposition with potentially even more fruitful and intriguing implications than mentioned in G&M’s book, we expressed some concern as to whether or not G&M will get their message through in the way their argument is formulated. By and large, our apprehension is triggered by a similar observation formulated by Elman (2013) who argues that some of G&M’s propositions about the set-theoretic nature of qualitative research are prescriptive while others are descriptive. We believe that in the discussions to follow, more clarity in distinguishing between what qualitative research currently is and what it ought to be would help to strengthen G&M’s vision of qualitative research as mainly being set-theoretic.
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30

N., Balamani A. Parvathi. "SEPARATION AXIOMS BY *𝛼 -CLOSED SETS". INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 5, № 10 (2016): 183–86. https://doi.org/10.5281/zenodo.159457.

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In this paper separation axioms of y<sup>*</sup>𝛼 -closed sets namely <sub>y</sub><sub>*</sub><sub>𝛼</sub>T<sub>c</sub>-space, <sub>y</sub><sub>*</sub><sub>𝛼</sub>T<sub>𝛼</sub>-space, <sub>g</sub><sub>𝛼</sub>T<sub>y</sub><sub>*</sub><sub>𝛼</sub> -space, <sub>𝛼</sub><sub>g</sub>T<sub>y</sub><sub>*</sub><sub>𝛼</sub> -space and <sub>y</sub><sub>g</sub>T<sub>y</sub><sub>*</sub><sub>𝛼</sub>-space are introduced and their properties are analyzed.
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31

Granirer, Edmond E. "Strong and Extremely Strong Ditkin sets for the Banach Algebras Apr(G) = Ap ⋂ Lr(G)." Canadian Journal of Mathematics 63, no. 1 (2011): 123–35. http://dx.doi.org/10.4153/cjm-2010-077-0.

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Abstract Let Ap(G) be the Figa-Talamanca, Herz Banach Algebra on G; thus A2(G) is the Fourier algebra. Strong Ditkin (SD) and Extremely Strong Ditkin (ESD) sets for the Banach algebras Apr (G) are investigated for abelian and nonabelian locally compact groups G. It is shown that SD and ESD sets for Ap(G) remain SD and ESD sets for Apr(G), with strict inclusion for ESD sets. The case for the strict inclusion of SD sets is left open.A result on the weak sequential completeness of A2(F) for ESD sets F is proved and used to show that Varopoulos, Helson, and Sidon sets are not ESD sets for A2r(G), yet they are such for A2(G) for discrete groups G, for any 1 ≤ r ≤ 2.A result is given on the equivalence of the sequential and the net definitions of SD or ESD sets for σ-compact groups.The above results are new even if G is abelian.
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32

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 ( &tau;<sub>i</sub> , &tau;<sub>j</sub> )* - Q* g closed set . We introduce and study a new class of spaces namely (&tau;<sub>i</sub> , &tau;<sub>j</sub> )* - Q*g T1/2 space and ( &tau;<sub>i</sub> , &tau;<sub>j</sub> )* - Q* g T3/4 space . Also we find some basic properties and applications of ( &tau;<sub>i</sub> , &tau;<sub>j</sub> )* - Q* g closed sets .
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33

Waner, Stefan. "Fixed Sets of Framed G-Manifolds." Transactions of the American Mathematical Society 298, no. 1 (1986): 421. http://dx.doi.org/10.2307/2000627.

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34

Costenoble, Steven R., Michael Steiner, and Stefan Waner. "Fixed Sets of Unitary G-Manifolds." Proceedings of the American Mathematical Society 121, no. 4 (1994): 1275. http://dx.doi.org/10.2307/2161243.

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35

Al-Kadi, Deena, and Rodyna A. Hosny. "G+-algebra, Filters and Upper sets." Applied Mathematics & Information Sciences 10, no. 6 (2016): 2131–36. http://dx.doi.org/10.18576/amis/100616.

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36

Costenoble, Steven R., Michael Steiner, and Stefan Waner. "Fixed sets of unitary $G$-manifolds." Proceedings of the American Mathematical Society 121, no. 4 (1994): 1275. http://dx.doi.org/10.1090/s0002-9939-1994-1198453-4.

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37

Waner, Stefan. "Fixed sets of framed $G$-manifolds." Transactions of the American Mathematical Society 298, no. 1 (1986): 421. http://dx.doi.org/10.1090/s0002-9947-1986-0857451-8.

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38

B, Shanmugaraj, та Kosalai G. "On Nano ∏g*β- Closed Sets". International Journal of Mathematics Trends and Technology 65, № 3 (2019): 47–51. http://dx.doi.org/10.14445/22315373/ijmtt-v65i3p507.

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39

B, Shanmugaraj, та S. Meena Devi. "On nano π* g* - Closed Sets". International Journal of Mathematics Trends and Technology 65, № 3 (2019): 85–91. http://dx.doi.org/10.14445/22315373/ijmtt-v65i3p514.

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40

Bulacu, D. "Injective modules graded by g-sets." Communications in Algebra 27, no. 7 (1999): 3537–43. http://dx.doi.org/10.1080/00927879908826644.

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41

Helen M, Pauline Mary, and Gayathri A. "g*-Closed Sets in Topological Spaces." International Journal of Mathematics Trends and Technology 6, no. 1 (2014): 60–74. http://dx.doi.org/10.14445/22315373/ijmtt-v6p506.

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42

Mahanta, J., and P. K. Das. "On Fuzzy g*s-Closed Sets." International Journal of Computer Applications 43, no. 2 (2012): 17–21. http://dx.doi.org/10.5120/6076-8187.

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43

Keshvardoost, Khadijeh, and Mojgan Mahmoudi. "Free functor from the category of G-nominal sets to that of 01-G-nominal sets." Soft Computing 22, no. 11 (2017): 3637–48. http://dx.doi.org/10.1007/s00500-017-2793-2.

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44

NETHAJI, OCHANAN, SUBRAMANIYAN DEVI, MAYANDI RAMESHPANDI, and RAJENDARAN PREMKUMAR. "DECOMPOSITIONS OF NANO g^#-CONTINUITY VIA IDEALIZATION." Journal of Science and Arts 23, no. 2 (2023): 377–80. http://dx.doi.org/10.46939/j.sci.arts-23.2-a05.

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In this paper we introduce the notions of αg^#-nI-open sets, η^#-nI-open sets, h^#-nI-open sets, g^# _t-nI-sets, g^# _(α^* )-nI-sets and g^# _S-nI-sets in ideal nano topological spaces and investigate some of their properties.
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45

Rajamani. "I_{\pi g}-Closed Sets and I_{\pi g}-Continuity." Journal of Advanced Research in Pure Mathematics 2, no. 4 (2010): 63–72. http://dx.doi.org/10.5373/jarpm.413.042010.

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46

Hassan, Javier, Sergio R. Canoy, Jr., and Alkajim A. Aradais. "Hop Independent Sets in Graphs." European Journal of Pure and Applied Mathematics 15, no. 2 (2022): 467–77. http://dx.doi.org/10.29020/nybg.ejpam.v15i2.4350.

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Let G be an undirected graph with vertex and edge sets V (G) and E(G), respectively. A set S ⊆ V (G) is a hop independent set of G if any two distinct vertices in S are not at a distance two from each other, that is, dG(v, w) 6= 2 for any distinct vertices v, w ∈ S. The maximum cardinality of a hop independent set of G, denoted by αh(G), is called the hop independence number of G. In this paper, we show that the absolute difference of the independence number and the hop independence number of a graph can be made arbitrarily large. Furthermore, we determine the hop independence numbers of some graphs including those resulting from some binary operations of graphs.
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47

Alikhani, Saeid, and Maryam Safazadeh. "Fair dominating sets of paths." Journal of Information and Optimization Sciences 44, no. 5 (2023): 855–64. http://dx.doi.org/10.47974/jios-1141.

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Let G = (V, E) be a simple graph. A dominating set of G is a subset D ⊆ V such that every vertex not in D is adjacent to at least one vertex in D. The cardinality of the smallest dominating set of G, denoted by g(G), is the domination number of G. For i ≥ 1, a i-fair dominating set (iFD-set) in G, is a dominating set S such that |N(v) ∩ D| = i for every vertex v ∈ V\D. A fair dominating set, in G is a iFD-set for some integer i ≥ 1. In this paper, we present the structure of fair dominating sets of a path and also we count the number of these sets.
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48

Yielding, Amy, Taylor Hunt, Joel Jacobs, Jazmine Juarez, Taylor Rhoton, and Heath Sell. "Inertia Sets of Semicliqued Graphs." Electronic Journal of Linear Algebra 37 (December 22, 2021): 747–57. http://dx.doi.org/10.13001/ela.2021.4933.

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In this paper, we investigate inertia sets of simple connected undirected graphs. The main focus is on the shape of their corresponding inertia tables, in particular whether or not they are trapezoidal. This paper introduces a special family of graphs created from any given graph, $G$, coined semicliqued graphs and denoted $\widetilde{K}G$. We establish the minimum rank and inertia sets of some $\widetilde{K}G$ in relation to the original graph $G$. For special classes of graphs, $G$, it can be shown that the inertia set of $G$ is a subset of the inertia set of $\widetilde{K}G$. We provide the inertia sets for semicliqued cycles, paths, stars, complete graphs, and for a class of trees. In addition, we establish an inertia set bound for semicliqued complete bipartite graphs.
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49

Jeyanthi, P., P. Nalayini, and T. Noiri. "g ∆ ∗ µ −closed sets in generalized topological spaces." Boletim da Sociedade Paranaense de Matemática 39, no. 3 (2021): 9–16. http://dx.doi.org/10.5269/bspm.39495.

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In this paper, we introduce some new classes of generalized closedsets called ∆ ∗µ −g− closed, ∆∗µ −g µ − closed and g ∆ ∗ µ − closed sets, which are relatedto the classes of g µ − closed sets, g − λ µ − closed sets and λ µ − g− closed sets. Weinvestigate their properties as well as the relations among these classes of generalizedclosed sets.
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50

Bors, Cristina, María V. Ferrer, and Salvador Hernández. "Bounded Sets in Topological Spaces." Axioms 11, no. 2 (2022): 71. http://dx.doi.org/10.3390/axioms11020071.

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Abstract:
Let G be a monoid that acts on a topological space X by homeomorphisms such that there is a point x0∈X with GU=X for each neighbourhood U of x0. A subset A of X is said to be G-bounded if for each neighbourhood U of x0 there is a finite subset F of G with A⊆FU. We prove that for a metrizable and separable G-space X, the bounded subsets of X are completely determined by the bounded subsets of any dense subspace. We also obtain sufficient conditions for a G-space X to be locally G-bounded, which apply to topological groups. Thereby, we extend some previous results accomplished for locally convex spaces and topological groups.
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