An Approach to the Concept of Soft Vieotoris Topology
Main Article Content
Abstract
In the present paper, we study the Vietoris topology in the context of soft set. Firstly, we investigate some aspects of first countability in the soft Vietoris topology. Then, we obtain some properties about its second countability.
Article Details
References
- M. Akda˘ g and F. Erol, On hyperspaces of soft sets, J. New Theory 7 (2015), 86-97.
- M. Akda˘ g and F. Erol, Remarks on hyperspaces of soft sets, J. Adv. Stud. Topol. 7 (2016), 1-11.
- H. Akta ¸ s and N. C ¸a˘ gman, Soft sets and soft groups, Inform. Sci. 177 (2007), 2726-2735.
- 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.
- M. Alimohammady, S. Jafari, S.P. Moshokoa and M.K. Kalleji, A note on properties of hypermetric spaces, J. Hyperstructures 3(2) (2014), 89-100.
- D. Andrijevic, M. Jelic and M. Mrsevic, Some properties of hyperspaces of Cech closure spaces, Filomat 24 (2010), 53-61.
- A. Aygüno˘ glu and H. Aygün, Some notes on soft topological spaces, Neural Comput. Appl. 21 (2012), 113-119.
- A. Bouziad, L. Hola and L. Zsilinszky, On hereditary Baireness of the Vietoris topology, Topology Appl. 115 (2001), 247-258.
- J. Chvalina, S. H. Mayerova and A. D. Nezhad, General actions of hyperstructures and some applications, An. St. Univ. Ovidius Constanta 21 (2013), 59-82.
- S. Das and S.K. Samanta, Soft metric, Ann. Fuzzy Math. Inform. 6(1) (2013), 77-94.
- Ë™ I. Demir and O.B. ¨ Ozbakir, Soft Hausdorff spaces and their some properties, Ann. Fuzzy Math. Inform. 8(5) (2014), 769-783.
- G. Di Maio and L. Hola, On hit-and-miss hyperspace topologies, Rend. Accad. Sci. Fis. Mat. Napoli 62 (1995), 103-124.
- A. Gavrilut and M. Agop, Approximation theorems for set multifunctions in Vietoris topology. Physical implications of regularity, Iran. J. Fuzzy syst. 12(1) (2013), 27-42.
- A.C ¸. Güler, E. D. Yildirim and O. B. ¨ Ozbakir, A fixed point theorem on soft G-metric spaces, J. Nonlinear Sci. Appl. 9 (2016), 885-894.
- L. Hola and S. Levi, Decomposition properties of hyperspace topologies, Set-Valued Anal. 5 (1997), 309-321.
- S. Hussain and B. Ahmad, Soft separation axioms in soft topological spaces, Hacet. J. Math. Stat. 44 (3) (2015), 559-568.
- W. Kai-ting, A new fixed point theorem in noncompact hyperconvex metric spaces and its application to saddle point problems, J. Math. Res. Expos. 28 (2008), 161-168.
- A. Kandil, O.A. Tantawy, S.A. El-Sheikh and A. Zakaria, New structures of proximity spaces, Inf. Sci. Lett. 3(3) (2014), 85-89.
- F. Lin, The Vietoris topology on rectifiable spaces, Semigroup Forum 88 (2014), 273-278.
- X. Ma, B. Huo and G. Liao, Chaos in hyperspace system, Chaos Solitons Fractals 40 (2009), 653-660.
- P.K. Maji, R. Biswas and A.R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003), 555-562.
- D. Molodtsov, Soft set theory-first results, Comput. Math. Appl. 37 (1999), 19-31.
- D. Molodtsov, V.Y. Leonov and D.V. Kovkov, Soft sets technique and its application, Nechetkie Sist. Myagkie Vychisl. 1 (2006), 8-39.
- S. Nazmul and S.K. Samanta, Neighbourhood properties of soft topological spaces, Ann. Fuzzy Math. Inform. 6(1) (2013), 1-15.
- D. Pei and D. Miao, From soft sets to information systems, In: Hu X, Liu Q, Skowron A, Lin TY, Yager RR, Zhang B, editors. Proceedings of Granular Computing-IEEE 2 (2005), 617-621.
- E. Peyghan, B. Samadi and A. Tayebi, Some results related to soft topological spaces, Facta Universitatis Ser. Math. Inform. 29(4) (2014), 325-336.
- J. Rodriguez-Lopez and S. Romaguera, The relationship between the Vietoris topology and the Hausdorff quasi- uniformity, Topology Appl. 124 (2002), 451-464.
- W. Rong, The countabilities of soft topological spaces, Int. J. Comput. Math. Sci. 6 (2012), 159-162.
- M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl. 61 (2011), 1786-1799.
- Q. R. Shakir, On Vietoris soft topology I, J. Sci. Res. 8(1) (2016), 13-19.
- I. Zorlutuna, M. Akdag, W.K. Min and S. Atmaca, Remarks on soft topological spaces, Ann. Fuzzy Math. Inform. 3(2) (2012), 171-185.
- L. Zsilinszky, Baire spaces and hyperspace topologies, Proc. Amer. Math. Soc. 124 (1996), 2575-2584.