Narzędzia help

Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
first last
cannonical link button

http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-9bc3f2ef-a2a0-4558-a990-fee45b278fe7

Czasopismo

Demonstratio Mathematica

Tytuł artykułu

Two types of separation axioms on supra softtopological spaces

Autorzy Al-shami, Tareq M.  El-Shafei, Mohammed E. 
Treść / Zawartość http://www.degruyter.com/view/j/dema
Warianty tytułu
Języki publikacji EN
Abstrakty
EN In 2011, Shabir and Naz [1] employed the notion of soft sets to introduce the concept of soft topologies; and in 2014, El-Sheikh and Abd El-Latif [2] relaxed the conditions of soft topologies to construct a wider and more general class, namely supra soft topologies. In this disquisition, we continue studying supra soft topologies by presenting two kinds of supra soft separation axioms, namely supra soft Ti-spaces and supra p-soft Ti-spaces for i= 0,1,2,3,4. These two types are formulated with respect to the ordinary points; and the difference between them is attributed to the applied non belong relations in their definitions. We investigate the relationships between them and their parametric supra topologies; and we provide many examples to separately elucidate the relationships among spaces of each type. Then we elaborate that supra p-soft Ti-spaces are finer than supra soft Ti-spaces in the case of i= 0,1,4; and we demonstrate that supra soft T3-spaces are finer than supra p-soft T3-spaces. We point out that supra p-softTi-axioms imply supra p-softTi−1, however, this characterization does not hold for supra soft Ti-axioms (see, Remark (3.30)). Also, we give a complete description of the concepts of supra p-soft Ti-spaces (i= 1,2) and supra p-soft regular spaces. Moreover, we define the finite product of supra soft spaces and manifest that the finite product of supra soft Ti (supra p-soft Ti) is supra soft Ti (supra p-soft Ti) for i= 0,1,2,3. After investigating some properties of these axioms in relation with some of the supra soft topological notions such as supra soft subspaces and enriched supra soft topologies, we explore the images of these axioms under soft S*-continuous mappings. Ultimately, we provide an illustrative diagram to show the interrelations between the initiated supra soft spaces.
Słowa kluczowe
PL przestrzeń topologiczna  
EN supra soft Ti-space   supra p-soft Ti-space   supra soft subspace   product supra soft spaces   supra soft topological space  
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2019
Tom Vol. 52, nr 1
Strony 147--165
Opis fizyczny Bibliogr. 40 poz., rys.
Twórcy
autor Al-shami, Tareq M.
autor El-Shafei, Mohammed E.
Bibliografia
[1] Shabir M., Naz M., On soft topological spaces, Comput. Math. Appl., 2011, 61, 1786–1799
[2] El-Sheikh S. A., Abd El-Latif A. M., Decompositions of some types of supra soft sets and soft continuity, International Journalof Mathematics Trends and Technology, 2014, 9, 37–56
[3] Molodtsov D., Soft set theory - first results, Comput. Math. Appl., 1999, 37, 19–31
[4] Cağman N., Enginoğ S., Soft matrix theory and its decision making, Comput. Math. Appl., 2010, 59, 3308–3314
[5] Yuksel S., Dizman T., Yildizdan G., Sert U., Application of soft sets to diagnose the prostate cancer risk, J. Inequal. Appl.,2013, 2013:229
[6] Karaaslan F., Soft classes and soft rough classes with applications in decision making, Math. Probl. Eng., 2016, Article ID1584528
[7] Aygünoǧlu A., Aygün H., Some notes on soft topological spaces, Neural Comput. & Applic., 2012, 21, 113–119
[8] Zorlutuna I., Akdag M., Min W. K., Atmaca S., Remarks on soft topological spaces, Ann. Fuzzy Math. Inform., 2012, 2, 171–185
[9] Nazmul S., Samanta S. K., Neighbourhood properties of soft topological spaces, Ann. Fuzzy Math. Inform., 2013, 6(1), 1–15
[10] Das S., Samanta S. K., Soft metric, Ann. Fuzzy Math. Inform., 2013, 6(1), 77–94
[11] Tantawy O., El-Sheikh S. A., Hamde S., Separation axioms on soft topological spaces, Ann. Fuzzy Math. Inform., 2016, 11,511–525
[12] Singh A., Noorie N. S., Remarks on soft axioms, Ann. Fuzzy Math. Inform., 2017, 14, 503–513
[13] Bayramov S., Aras C. G., A new approach to separability and compactness in soft topological spaces, TWMS J. Pure Appl.Math., 2018, 9, 82–93
[14] El-Shafei M. E., Abo-Elhamayel M., Al-shami T. M., Partial soft separation axioms and soft compac spaces, Filomat, 2018,32(13), 4755–4771
[15] Al-shami T. M., Corrigendum to "On soft topological space via semi-open and semi-closed soft sets, Kyungpook Mathemat-ical Journal, 54(2014), 221–236", Kyungpook Math. J., 2018, 58(3), 583–588
[16] Al-shami T. M., Corrigendum to "Separation axioms on soft topological spaces, Ann. Fuzzy Math. Inform., 11(4) (2016) 511–525", Ann. Fuzzy Math. Inform., 2018, 15(3), 309–312
[17] El-Shafei M. E., Abo-Elhamayel M., Al-shami T. M., Two notes on "On soft Hausdorff spaces", Ann. Fuzzy Math. Inform., 2018,16(3), 333–336
[18] Al-shami T. M., Comments on "Soft mappings spaces", The Scientific World Journal, 2019, Article ID 6903809
[19] Mashhour A. S., Allam A. A., Mahmoud F. S., Khedr F. H., On supra topological spaces, Indian J. Pure Appl. Math., 1983, 14(4),502–510
[20] Al-shami T. M., Some results related to supra topological spaces, J. Adv. Stud. Topol., 2016, 7, 283–294
[21] El-Shafei M. E., Abo-Elhamayel M., Al-shami T. M., On supra R-open sets and some applications on topological spaces, Journal of Progressive Research in Mathematics, 2016, 8(2), 1237–1248
[22] Kozae A. M., Shokry M., Zidan M., Supra topologies for digital plane, AASCIT Communications, 2016, 3(1), 1–10
[23] Al-shami T. M., On supra semi open sets and some applications on topological spaces, J. Adv. Stud. Topol., 2017, 8(2),144–153
[24] Al-shami T. M., Utilizing supra α-open sets to generate new types of supra compact and supra Lindelöf spaces, Facta Univ.Ser. Math. Inform., 2017, 32(1), 151–162
[25] Al-shami T. M., Supra semi-compactness via supra topological spaces, Journal of Taibah University for Science, 2018, 12(3),338–343
[26] El-Shafei M. E., Abo-Elhamayel M., Al-shami T. M., Further notions related to new operators and compactness via supra softtopological spaces, International Journal of Advances in Mathematics, 2019, 1, 44–60
[27] Abd El-latif A. M., Karatas S., Supra b-open soft sets and supra b-soft continuity on soft topological spaces, Journal of Mathematics and Computer Applications Research, 2015, 5(1), 1–18
[28] Kandil A., Tantawy O. A. E., El-Sheikh S. A., Abd El-latif A. M., Notes on γ-soft operator and some counterexamples on (supra) soft continuity, Ann. Fuzzy Math. Inform., 2015, 10(2), 203–213
[29] Abd El-Latif A. M., Hosny R. A., Supra semi open soft sets and associated soft separation axioms, Appl. Math. Inf. Sci., 2016,10(6), 2207–2215
[30] Abd El-Latif A. M., Hosny R. A., Supra open soft sets and associated soft separation axioms, International Journal of Advancesin Mathematics, 2017, 2(6), 68–81
[31] Khattak A. M., Younas M., Khan G. A., Ur-Rehman M., Nadeem S., Safeer M., P-separation axioms in supra soft topological spaces, Matrix Science Mathematic (MSMK), 2018, 2(2), 07–10
[32] Hosny R. A., Al-Kadi D., Supra soft topology generated from soft topology via soft stack, South Asian Journal of Mathematics, 2017, 7(1), 25–33
[33] Ali M. I., Feng F., Liu X., Min W. K., Shabir M., On some new operations in soft set theory, Comput. Math. Appl., 2009, 57,1547–1553
[34] Maji P. K., Biswas R., Roy R., Soft set theory, Comput. Math. Appl., 2003, 45, 555–562
[35] Feng F., Li Y. M., Davvaz B., Ali M. I., Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Comput,2010, 14, 899–911
[36] Qin K., Hong Z., On soft equality, J. Comput. Appl. Math., 2010, 234, 1347–1355
[37] Abbas M., Ali M. I., Romaguera S., Generalized operations in soft set theory via relaxed conditions on parameters, Filomat, 2017, 31(19) 5955–5964.
[38] Al-shami T. M., El-Shafei M. E., Abo-Elhamayel M., On soft topological ordered spaces, Journal of King Saud University-Science, https://doi.org/10.1016/j.jksus.2018.06.005
[39] Karaaslan F., Çaǧman N., Enginoǧlu S., Soft lattices, Journal of New Results in Science, 2012, 1, 5–17
[40] Al-shami T. M., Soft somewhere dense sets on soft topological spaces, Commun. Korean Math. Soc., 2018, 33(4), 1341–1356
Uwagi
PL Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Kolekcja BazTech
Identyfikator YADDA bwmeta1.element.baztech-9bc3f2ef-a2a0-4558-a990-fee45b278fe7
Identyfikatory
DOI 10.1515/dema-2019-0016