On elementary soft compact topological spaces

İsmet Altıntaş; Arzıgul İmankulova

doi:10.51354/mjen.946652

EN

On elementary soft compact topological spaces

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.

Keywords

Soft set, soft element, elementary operations, 𝜖-soft compactness.

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.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

İsmet Altıntaş ^*
0000-0002-9925-8954
Kyrgyzstan

Arzıgul İmankulova This is me
Kyrgyzstan

Publication Date

December 6, 2021

Submission Date

June 1, 2021

Acceptance Date

June 10, 2021

Published in Issue

Year 2021 Volume: 9 Number: 2

DOI

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

IZ

https://izlik.org/JA69YW37WT

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

1.Altıntaş İ, İmankulova A. On elementary soft compact topological spaces. MJEN. 2021;9(2):198-205. doi:10.51354/mjen.946652

Chicago

Altıntaş, İsmet, and Arzıgul İmankulova. 2021. “On Elementary Soft Compact Topological Spaces”. MANAS Journal of Engineering 9 (2): 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

[1]İ. Altıntaş and A. İmankulova, “On elementary soft compact topological spaces”, MJEN, vol. 9, no. 2, pp. 198–205, Dec. 2021, doi: 10.51354/mjen.946652.

ISNAD

Altıntaş, İsmet - İmankulova, Arzıgul. “On Elementary Soft Compact Topological Spaces”. MANAS Journal of Engineering 9/2 (December 1, 2021): 198-205. https://doi.org/10.51354/mjen.946652.

JAMA

1.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, Dec. 2021, pp. 198-05, doi:10.51354/mjen.946652.

Vancouver

1.İsmet Altıntaş, Arzıgul İmankulova. On elementary soft compact topological spaces. MJEN. 2021 Dec. 1;9(2):198-205. doi:10.51354/mjen.946652

Cited By

Topology of soft partial metric spaces

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https://doi.org/10.1007/s00500-025-10870-y

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