On elementary soft compact topological spaces
Year 2021,
, 198 - 205, 06.12.2021
İsmet Altıntaş
,
Arzıgul İmankulova
Abstract
This paper is a work on elementary soft (𝜖-soft) compact spaces. We first define the cofinite 𝜖-
soft compact space and prove that the image of an 𝜖-soft compact space under a soft continuous
mapping is 𝜖-soft compact space. We then examine the relationship between 𝜖-soft compact
space and classical compact space and give an illustrative example.
References
- Molodtsov D., Soft set theory-first results, Comput. Math. Appl., 37, (1999), 19-31.
- Maji P. K., Biswas R. and Roy A. R., Soft set theory, Comput. Math. Appl., 45, (2003), 555-562.
- Maji P. K., Roy A. R. and Biswas R., An application of soft sets in a decision making problem, Comput. Math. Appl., 44, (2002), 1077-1083.
- Chen D., Tsang E. C. C., Yeung D. S. and Wang X., The parameterization reduction of soft sets and its applications, Comput. Math. Appl., 49, (2005), 757-763.
- Pei D. and Miao D., From soft sets to information systems, 2005 IEEE International Conference on Granular Computing, vol. 2, IEEE, 2005, pp. 617–621.
- Kong Z., Jia W., Zhang G. and Wang L., Normal parameter reduction in soft set based on particle swarm optimization algorithm, Appl. Math. Model., 39, (2015), 4808-4820.
- Zou Y. and Xiao Z., Data analysis approaches of soft sets under incomplete information, Knowledge-Based Systems, 21, (2008), 941-945.
- Shabir M. and Naz M., On soft topological spaces, Comput. Math. Appl., 61, (2011), no. 7, 1786-1799.
- Aygünoğlu A. and Aygün H., Some notes on soft topological spaces, Neural Computing and Applications, 21, (2012), 113-119.
- Babitha K. V. and John S. J., Studies on soft topological spaces, J. Intell. Fuzzy Syst., 28, (2015), 1713-1722.
- Çetkin V. and Aygün H., On convergence of soft nets, J. Mult.-Valued Logic Soft Comput., 26, (2016), 175-187.
- Matejdes M., Soft topological space and topology on the cartesian product, Hacet. J. Math. Stat., 45, (2016), 1091-1100.
- Pazar Varol B. and Aygün H., Soft sets over power sets: Generalities and applications to topology, J. Intell. Fuzzy Syst, 29, (2015), 389–395.
- Yang H.-L., Liao X. and Li S.-G., On soft continuous mappings and soft connectedness of soft topological spaces, Hacet. J. Math. Stat., 44, (2015), 385-398.
- Zorlutuna İ., Akdağ M., Min W. K. and Atmaca S., Remarks on soft topological spaces, Ann. Fuzzy Math. Inform., 3, (2012), 171-185.
- Das S. and Samanta S. K., Soft real sets, soft real numbers and their properties, J. Fuzzy Math., 20, (2012), 551-576.
- Das S. and Samanta S. K., On soft complex sets and soft complex numbers, J. Fuzzy Math., 21, (2013), 195-216.
- Das S., Majumdar P. and Samanta S. K., On soft linear spaces and soft normed linear spaces, Ann. Fuzzy Math. Inform., 9, (2015), 91-109.
- Das S. and Samanta S. K., On soft metric spaces, J. Fuzzy Math., 21, (2013), 707-734.
- Das S. and Samanta S. K., Soft linear operators in soft normed linear spaces, Ann. Fuzzy Math. Inform., 6, (2013), 295-314.
- Abbas M., Murtaza G. and Romaguera S., On the fixed point theory of soft metric spaces, Fixed Point Theory Appl., (2016), 17.
- Leyew B. T. and Abbas M., A soft version of the knaster–tarski fixed point theorem with applications, J. Fixed Point Theory Appl., (2017), 1-15.
- Hosseinzadeh H., Fixed point theorems on soft metric spaces, J. Fixed Point Theory Appl., (2016), 1-23.
- Dağıstan Ş. et al., An introduction to soft cone metric spaces and some fixed Point theorems, MANAS Journal of Engineering, 5 (Issue 3), (2017), 69-89.
- Altintas I., Simsek D. and Taskopru K., Topology of soft cone metric spaces, : AIP Conference Proceedings 1880, 030006 (2017), 1-6 doi: 10.1063/1.5000605,
- Altıntaş İ. and Taşköprü K., Compactness of soft cone metric space and fixed point theorems related to diametrically contractive mapping, Turkish Journal of Mathematics, 44, (2020), 2199 – 221.
- Chiney M. and Samanta S.K., Soft topology redefined, J. Fuzzy Math., 27(2), (2019), 459-486.
- Taşköprü K. and Altıntaş İ., A new approach for soft topology and soft function via soft element, Math Meth. Appl. Sci., (2021), 44, 7556–7570.
- Altıntaş İ., Taşköprü K. and Selvi B., Countable and separable elementary soft topological space, Math Meth. Appl. Sci., (2021), 44, 7811–7819.
- Bousselsal M. and Saadi A., Soft elementary compact in soft elementary topology, arXiv:1803.11448v2, Math GM, (2018).
- Roy S. and Chiney M., On compactness and connectedness in redefined soft topological spaces, International Journal of Pure and Applied Mathematics, 120(5), (2019), 1505-1528.
Year 2021,
, 198 - 205, 06.12.2021
İsmet Altıntaş
,
Arzıgul İmankulova
References
- Molodtsov D., Soft set theory-first results, Comput. Math. Appl., 37, (1999), 19-31.
- Maji P. K., Biswas R. and Roy A. R., Soft set theory, Comput. Math. Appl., 45, (2003), 555-562.
- Maji P. K., Roy A. R. and Biswas R., An application of soft sets in a decision making problem, Comput. Math. Appl., 44, (2002), 1077-1083.
- Chen D., Tsang E. C. C., Yeung D. S. and Wang X., The parameterization reduction of soft sets and its applications, Comput. Math. Appl., 49, (2005), 757-763.
- Pei D. and Miao D., From soft sets to information systems, 2005 IEEE International Conference on Granular Computing, vol. 2, IEEE, 2005, pp. 617–621.
- Kong Z., Jia W., Zhang G. and Wang L., Normal parameter reduction in soft set based on particle swarm optimization algorithm, Appl. Math. Model., 39, (2015), 4808-4820.
- Zou Y. and Xiao Z., Data analysis approaches of soft sets under incomplete information, Knowledge-Based Systems, 21, (2008), 941-945.
- Shabir M. and Naz M., On soft topological spaces, Comput. Math. Appl., 61, (2011), no. 7, 1786-1799.
- Aygünoğlu A. and Aygün H., Some notes on soft topological spaces, Neural Computing and Applications, 21, (2012), 113-119.
- Babitha K. V. and John S. J., Studies on soft topological spaces, J. Intell. Fuzzy Syst., 28, (2015), 1713-1722.
- Çetkin V. and Aygün H., On convergence of soft nets, J. Mult.-Valued Logic Soft Comput., 26, (2016), 175-187.
- Matejdes M., Soft topological space and topology on the cartesian product, Hacet. J. Math. Stat., 45, (2016), 1091-1100.
- Pazar Varol B. and Aygün H., Soft sets over power sets: Generalities and applications to topology, J. Intell. Fuzzy Syst, 29, (2015), 389–395.
- Yang H.-L., Liao X. and Li S.-G., On soft continuous mappings and soft connectedness of soft topological spaces, Hacet. J. Math. Stat., 44, (2015), 385-398.
- Zorlutuna İ., Akdağ M., Min W. K. and Atmaca S., Remarks on soft topological spaces, Ann. Fuzzy Math. Inform., 3, (2012), 171-185.
- Das S. and Samanta S. K., Soft real sets, soft real numbers and their properties, J. Fuzzy Math., 20, (2012), 551-576.
- Das S. and Samanta S. K., On soft complex sets and soft complex numbers, J. Fuzzy Math., 21, (2013), 195-216.
- Das S., Majumdar P. and Samanta S. K., On soft linear spaces and soft normed linear spaces, Ann. Fuzzy Math. Inform., 9, (2015), 91-109.
- Das S. and Samanta S. K., On soft metric spaces, J. Fuzzy Math., 21, (2013), 707-734.
- Das S. and Samanta S. K., Soft linear operators in soft normed linear spaces, Ann. Fuzzy Math. Inform., 6, (2013), 295-314.
- Abbas M., Murtaza G. and Romaguera S., On the fixed point theory of soft metric spaces, Fixed Point Theory Appl., (2016), 17.
- Leyew B. T. and Abbas M., A soft version of the knaster–tarski fixed point theorem with applications, J. Fixed Point Theory Appl., (2017), 1-15.
- Hosseinzadeh H., Fixed point theorems on soft metric spaces, J. Fixed Point Theory Appl., (2016), 1-23.
- Dağıstan Ş. et al., An introduction to soft cone metric spaces and some fixed Point theorems, MANAS Journal of Engineering, 5 (Issue 3), (2017), 69-89.
- Altintas I., Simsek D. and Taskopru K., Topology of soft cone metric spaces, : AIP Conference Proceedings 1880, 030006 (2017), 1-6 doi: 10.1063/1.5000605,
- Altıntaş İ. and Taşköprü K., Compactness of soft cone metric space and fixed point theorems related to diametrically contractive mapping, Turkish Journal of Mathematics, 44, (2020), 2199 – 221.
- Chiney M. and Samanta S.K., Soft topology redefined, J. Fuzzy Math., 27(2), (2019), 459-486.
- Taşköprü K. and Altıntaş İ., A new approach for soft topology and soft function via soft element, Math Meth. Appl. Sci., (2021), 44, 7556–7570.
- Altıntaş İ., Taşköprü K. and Selvi B., Countable and separable elementary soft topological space, Math Meth. Appl. Sci., (2021), 44, 7811–7819.
- Bousselsal M. and Saadi A., Soft elementary compact in soft elementary topology, arXiv:1803.11448v2, Math GM, (2018).
- Roy S. and Chiney M., On compactness and connectedness in redefined soft topological spaces, International Journal of Pure and Applied Mathematics, 120(5), (2019), 1505-1528.