Research Article
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On elementary soft compact topological spaces

Year 2021, , 198 - 205, 06.12.2021
https://doi.org/10.51354/mjen.946652

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
https://doi.org/10.51354/mjen.946652

Abstract

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.
There are 31 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

İsmet Altıntaş 0000-0002-9925-8954

Arzıgul İmankulova This is me

Publication Date December 6, 2021
Published in Issue Year 2021

Cite

APA Altıntaş, İ., & İmankulova, A. (2021). On elementary soft compact topological spaces. MANAS Journal of Engineering, 9(2), 198-205. https://doi.org/10.51354/mjen.946652
AMA Altıntaş İ, İmankulova A. On elementary soft compact topological spaces. MJEN. December 2021;9(2):198-205. doi:10.51354/mjen.946652
Chicago Altıntaş, İsmet, and Arzıgul İmankulova. “On Elementary Soft Compact Topological Spaces”. MANAS Journal of Engineering 9, no. 2 (December 2021): 198-205. https://doi.org/10.51354/mjen.946652.
EndNote Altıntaş İ, İmankulova A (December 1, 2021) On elementary soft compact topological spaces. MANAS Journal of Engineering 9 2 198–205.
IEEE İ. Altıntaş and A. İmankulova, “On elementary soft compact topological spaces”, MJEN, vol. 9, no. 2, pp. 198–205, 2021, doi: 10.51354/mjen.946652.
ISNAD Altıntaş, İsmet - İmankulova, Arzıgul. “On Elementary Soft Compact Topological Spaces”. MANAS Journal of Engineering 9/2 (December 2021), 198-205. https://doi.org/10.51354/mjen.946652.
JAMA Altıntaş İ, İmankulova A. On elementary soft compact topological spaces. MJEN. 2021;9:198–205.
MLA Altıntaş, İsmet and Arzıgul İmankulova. “On Elementary Soft Compact Topological Spaces”. MANAS Journal of Engineering, vol. 9, no. 2, 2021, pp. 198-05, doi:10.51354/mjen.946652.
Vancouver Altıntaş İ, İmankulova A. On elementary soft compact topological spaces. MJEN. 2021;9(2):198-205.

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