Two new forms of ordered soft separation axioms

• Autorzy: Al-shami Tareq M. , El-Shafei Mohammed E.

Identyfikatory

DOI

10.1515/dema-2020-0002

• Języki publikacji: EN

Abstrakty

EN

The goal of this work is to introduce and study two new types of ordered soft separation axioms, namely soft Ti-ordered and strong soft Ti-ordered spaces (i = 0, 1, 2, 3, 4). These two types are formulated with respect to the ordinary points and the distinction between them is attributed to the nature of the monotone neighborhoods. We provide several examples to elucidate the relationships among these concepts and to show the relationships associate them with their parametric topological ordered spaces and p-soft Ti-ordered spaces. Some open problems on the relationships between strong soft Ti-ordered and soft Ti-ordered spaces (i = 2, 3, 4) are posed. Also, we prove some significant results which associate both types of the introduced ordered axioms with some notions such as finite product soft spaces, soft topological and soft hereditary properties. Furthermore, we describe the shape of increasing (decreasing) soft closed and open subsets of soft regularly ordered spaces; and demonstrate that a condition of strong soft regularly ordered is sufficient for the equivalence between p-soft T1-ordered and strong soft T1-ordered spaces. Finally, we establish a number of findings that associate soft compactness with some ordered soft separation axioms initiated in this work.

Słowa kluczowe

EN

monotone soft open set; monotone soft neighborhood; soft Ti-ordered spaces; strong soft Ti-ordered spaces (i = 0, 1, 2, 3, 4)

PL

zbiór otwarty; sąsiedztwo; przestrzeń uporządkowana; aksjomaty oddzielania; przestrzeń topologiczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2020
• Tom: Vol. 53, nr 1
• Strony: 8--26
• Opis fizyczny: Bibliogr. 40 poz., rys.

Twórcy

autor

Al-shami Tareq M.

• Department of Mathematics, Sana’a University, Sana’a, Yemen

autor

El-Shafei Mohammed E.

• Department of Mathematics, Mansoura University, Mansoura, Egypt

Bibliografia

• [1] L. Nachbin, Topology and ordered, D. Van Nostrand Inc. Princeton, New Jersey, 1965.
• [2] S.D. McCartan, Separation axioms for topological ordered spaces, Math. Proc. Camb. Philos. Soc. 64 (1968), 965–973.
• [3] S.D. Arya and K. Gupta, New separation axioms in topological ordered spaces, Indian J. Pure Appl. Math. 22 (1991), 461–468.
• [4] P. Das, Separation axioms in ordered spaces, Soochow Journal of Mathematics 30 (2004), no. 4, 447–454.
• [5] M.E. El-Shafei, M. Abo-Elhamayel, and T.M. Al-shami, Strong separation axioms in supra topological ordered spaces, Math. Sci. Lett. 6 (2017), no.3, 271–277.
• [6] L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338–353.
• [7] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182–190.
• [8] A.K. Katsaras, Ordered fuzzy topological spaces, J. Math. Anal. Appl. 84 (1981), 44–58.
• [9] D. Molodtsov, Soft set theory – First results, Comput. Math. Appl. 37 (1999), 19–31.
• [10] M.I. Ali, F. Feng, X. Liu, W.K. Min, and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009), 1547–1553.
• [11] P.K. Maji, R. Biswas, and R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003), 555–562.
• [12] M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl. 61 (2011), 1786–1799.
• [13] A. Aygünoğlu and H. Aygün, Some notes on soft topological spaces, Neural Comput. & Applic. 21 (2012), 113–119.
• [14] T. Hida, A comprasion of two formulations of soft compactness, Ann. Fuzzy Math. Inform. 8 (2014), no.4, 511–524.
• [15] T.M. Al-shami, M.E. El-Shafei, and M. Abo-Elhamayel, Almost soft compact and approximately soft Lindelöf spaces, J. Taibah Univ. Sci. 12 (2018), no.5, 620–630.
• [16] T.M. Al-shami and M.E. El-Shafei, On soft compact and soft Lindelöf spaces via soft pre-open sets, Ann. Fuzzy Math. Inform. 17 (2019), no.1, 79–100.
• [17] T.M. Al-shami, M.E. El-Shafei, and M. Abo-Elhamayel, Seven generalized types of soft semi-compact spaces, Korean J. Math. 27 (2019), no.3, 661–690.
• [18] T.M. Al-shami, M.A. Al-Shumrani, and B.A. Asaad, Some generalized forms of soft compactness and soft Lindelöfness via soft α-open sets, Italian J. Pure Appl. Math. 43 (2020), 680–704.
• [19] 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.
• [20] W.K. Min, A note on soft topological spaces, Comput. Math. Appl. 62 (2011), 3524–3528.
• [21] 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.
• [22] T.M. Al-shami, Corrigendum to "Separation axioms on soft topological spaces", Ann. Fuzzy Math. Inform. 11 (2016), no. 4, 511–525, Ann. Fuzzy Math. Inform. 15 (2018), no.3, 309–312.
• [23] M.E. El-Shafei, M. Abo-Elhamayel, and T.M. Al-shami, Two notes on "On soft Hausdorff spaces", Ann. Fuzzy Math. Inform. 16 (2018), no.3, 333–336.
• [24] 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.
• [25] T.M. Al-shami, Comments on "Soft mappings spaces", The Scientific World Journal 2019 (2019), Article ID 6903809.
• [26] T.M. Al-shami and L.D.R. Kočinac, The equivalence between the enriched and extended soft topologies, Appl. Comput. Math. 18 (2019), no.2, 149–162.
• [27] T.M. Al-shami and M.E. El-Shafei, Two types of separation axioms on supra soft topological spaces, Demonstr. Math. 52 (2019), no.1, 147–165.
• [28] S. Bayramov and C.G. Aras, A new approach to separability and compactness in soft topological spaces, TWMS J. Pure Appl. Math. 9 (2018), 82–93.
• [29] 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.
• [30] T.M. Al-shami and M.E. El-Shafei, On supra soft topological ordered spaces, Arab Journal of Basic and Applied Sciences 26 (2019), no.1, 433–445.
• [31] O. Tantawy, S.A. El-Sheikh, and S. Hamde, Separation axioms on soft topological spaces, Ann. Fuzzy Math. Inform. 11 (2016), 511–525.
• [32] A. Singh and N.S. Noorie, textitRemarks on soft axioms, Ann. Fuzzy Math. Inform. 14 (2017), 503–513.
• [33] C.G. Aras and S. Bayramov, A new approach to separability and compactness in soft topological spaces, TWMS J. Pure Appl. Math. 9 (2018), no.1, 82–93.
• [34] 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 (2020), 5377–5387.
• [35] S. Nazmul and S.K. Samanta, Neigbourhood properties of soft topological spaces, Ann. Fuzzy Math. Inform. 6 (2013), no.1, 1–15.
• [36] F. Feng, Y.M. Li, B. Davvaz, and M.I. Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Comput. 14 (2010), 899–911.
• [37] K.V. Babitha and J.J. Sunil, Soft set relations and functions, Comput. Math. Appl. 60 (2010), no.7, 1840–1849.
• [38] J.L. Kelley, General topology, Springer Verlag, 1975.
• [39] I. Zorlutuna, M. Akdag, W.K. Min, and S. Atmaca, Remarks on soft topological spaces, Ann. Fuzzy Math. Inform. 2 (2012), 171–185.
• [40] S.A. El-Sheikh and A.M. Abd El-Latif, Decompositions of some types of supra soft sets and soft continuity, Int. J. of Math. Trends Technol. 9 (2014), 37–56.

Uwagi

PL

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