On soft pc-separation axioms

• Autorzy: Hamko Qumri H. , Ahmed Nehmat K. , Khalaf Alias B.

Identyfikatory

DOI

10.1515/dema-2020-0003

• Języki publikacji: EN

Abstrakty

EN

Many mathematicians defined and studied soft separation axioms and soft continuity in soft spaces by using ordinary points of a topological space X. Also, some of them studied the same concepts by using soft points. In this paper, we introduce the concepts of soft pc−Ti and soft pc−T⁎i, i=0,1,2 by using the concept of soft pc-open sets in soft topological spaces. We explore several properties of such spaces. We also investigate the relationship among these spaces and provide a counter example when it is needed.

Słowa kluczowe

EN

soft pc-open set; soft pc − Ti spaces; separation axioms; soft topological spaces

PL

miękki zbiór otwarty; aksjomaty oddzielania; przestrzenie topologiczne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2020
• Tom: Vol. 53, nr 1
• Strony: 67--79
• Opis fizyczny: Bibliogr. 29 poz.

Twórcy

autor

Hamko Qumri H.

• Department of Mathematics, College of Education, Salahaddin University, Kurdistan-Region, Iraq

autor

Ahmed Nehmat K.

• Department of Mathematics, College of Education, Salahaddin University, Kurdistan-Region, Iraq

autor

Khalaf Alias B.

• Department of Mathematics, College of Science, University of Duhok, Kurdistan-Region, Iraq

Bibliografia

• [1] D. Molodtsov, Soft set theory-first results, Comput. Math. Appl. 37 (1999), 19-31.
• [2] A. Ghareeb, Soft weak Baire spaces, J. Egyptian Math. Soc.26 (2018), no. 3, 395-405, DOI: 10.21608/joems.2018.2729.1028.
• [3] A. H. Zakari, A. Ghareeb, and S. Omran, On soft weak structures, Soft Comput. 21 (2017), 2553-2559, DOI: 10.1007/ s00500-016-2136-8.
• [4] M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl. 61 (2011), 1786-1799, DOI: 10.1016/ j.camwa.2011.02.006.
• [5] F.-G. Shi and B. Pang, A note on soft topological spaces, Iran. J. Fuzzy Syst. 12 (2015), no. 5, 149-155.
• [6] D. N. Georgiou, A. C. Megaritis, and V. I. Petropoulos, On soft topological spaces, Appl. Math. Inf. Sci. 7 (2013), no. 2, 1889-1901.
• [7] I. Zorlutuna, M. Akdag, W. K. Min, and S. Atmaca, Remarks on soft topological spaces, Ann. Fuzzy Math. Inform. 3(2012), no. 2, 171-185.
• [8] I. Zorlutuna and H. Cakir, On continuity of soft mappings, Appl. Math. Inf. Sci. 9 (2015), no. 1, 403-409.
• [9] S. Hussain and B. Ahmad, Some properties of soft topological spaces, Comput. Math. Appl. 62 (2011), 4058-4067.
• [10] S. Hussain and B. Ahmad, Soft separation axioms in soft topological spaces, Hacet. J. Math. Stat. 44 (2015), no. 3, 559-568.
• [11] S. Bayramov and C. G. Aras, A new approach to separability and compactness in soft topological spaces, TWMS J. Pure Appl. Math. 9 (2018), no. 1, 82-93.
• [12] M.E. El-Shafei, M. Abo-Elhamayel, and T.M. Al-Shami, Partial soft separation axioms and soft compact spaces, Filomat 32 (2018), no. 13, 4755-4771.
• [13] Q. H. Hamko and N. K. Ahmed, Characterizations of špc -open sets and špc -almost continuous mappingin soft topological spaces, Eurasian J. Sci. Eng. 4 (2018), no. 2, 192-209.
• [14] T. M. Al-shami and L. D. R. Kocinac, The equivalence between the enriched and extended soft topologies, Appl. Comput. Math. 18 (2019), no. 2, 149-162.
• [15] T. M. Al-shami, M. E. El-Shafei, and M. Abo-Elhamayel, On soft topological ordered spaces, J. King Saud Univ. Sci. 31 (2019), no. 4, 556-566, DOI: 10.1016/j.jksus.2018.06.005.
• [16] T. M. Al-shami and M. E. El-Shafei, On supra soft topological ordered spaces, Arab J. Basic Appl. Sci. 26 (2019), no. 1, 433-445.
• [17] T. M. Al-shami and M. E. El-Shafei, Two new types of separation axioms on supra soft separation spaces, Demonst. Math. 52 (2019), no. 1, 147-165.
• [18] T. M. Al-shami and M. E. El-Shafei, Partial belong relation on soft separation axioms and decision making problem: two birds with one stone, Soft Comput. 24 (2019), 5377-5387.
• [19] T. M. Al-shami, Comments on “soft mappings spaces”, Sci. World J. 2019 (2019), 2, Article ID 6903809, DOI: 10.1155/ 2019/6903809.
• [20] P. K. Maji, R. Biswas, and R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003), 555-562.
• [21] M. Akdag and A. Ozkan, On soft preopen sets and soft pre-separation axioms, Gazi Univ. J. Sci. 27 (2014), no. 4, 1077-1083.
• [22] G. Ilango and M. Ravindran, On soft pre-open sets in soft topological spaces, Int. J. Math. Research 5 (2013), no 4, 399-409.
• [23] M. Ravindran and G. Ilango, A note on soft pre-pen sets, Int. J. Pure Appl. Math. 106 (2016), no. 5, 63-78.
• [24] N. K. Ahmed and Q. H. Hamko, špc-open sets and špc-continuity in soft topological spaces, ZANCO J. Pure Appl. Sci. 30 (2017), no. 6, 72-84.
• [25] O. Gocur and A. Kopuzlu, On soft separation axioms, Ann. Fuzzy Math. Inform. 9 (2015), no. 5, 817-822.
• [26] T. M. Al-shami, Corrigendum to “On soft topological space via semi-open and semi-closed soft sets, Kyungpook Math. J. 54 (2014), 221–236”, Kyungpook Math. J. 58 (2018), no. 3, 583-588.
• [27] T. M. Al-shami, Investigation and corrigendum to some results related to g-soft equality and gf-soft equality relations, Filomat 33 (2019), no. 11, 3375-3383.
• [28] M. E. El-Shafei, M. Abo-Elhamayel, and T. M. Al-shami, Two notes on “On soft Hausdorff spaces”, Ann. Fuzzy Math. Inf. 16 (2018), no. 3, 333-336.
• [29] T. M. Al-shami, Corrigendum to “Separation axioms on soft topological spaces, Ann. Fuzzy Math. Inf. 11 (2016), no. 4, 511–525”, Ann. Fuzzy Math. Inf. 15 (2018), no. 3, 309-312.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).