The soft topology of soft \(\omega ^{\ast }\)-open sets and soft almost Lindelofness
Volume 30, Issue 3, pp 281--289
http://dx.doi.org/10.22436/jmcs.030.03.07
Publication Date: February 02, 2023
Submission Date: November 10, 2022
Revision Date: November 27, 2022
Accteptance Date: December 30, 2022
Authors
S. Al Ghour
- Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan .
Abstract
In this paper, We use the soft closure operator to
introduce soft \(\omega ^{\ast }\)-open sets as a new class of soft sets. We
prove that this class of soft sets forms a soft topology that lies strictly
between the soft topology of soft \(\theta \)-open sets and the soft topology
of soft \(\omega \)-open sets. Also, we show that the soft topology of soft \(%
\omega ^{\ast }\)-open sets contain the soft co-countable topology and is
independent of the topology of soft open sets. Furthermore, several results
regarding soft almost Lindelofness are given. In addition to these, we
investigate the correspondences between the novel notions in soft topology
and their general topological analogs.
Share and Cite
ISRP Style
S. Al Ghour, The soft topology of soft \(\omega ^{\ast }\)-open sets and soft almost Lindelofness, Journal of Mathematics and Computer Science, 30 (2023), no. 3, 281--289
AMA Style
Ghour S. Al, The soft topology of soft \(\omega ^{\ast }\)-open sets and soft almost Lindelofness. J Math Comput SCI-JM. (2023); 30(3):281--289
Chicago/Turabian Style
Ghour, S. Al. "The soft topology of soft \(\omega ^{\ast }\)-open sets and soft almost Lindelofness." Journal of Mathematics and Computer Science, 30, no. 3 (2023): 281--289
Keywords
- Soft \(\omega \)-open sets
- soft \(\theta \)-open sets
- soft regularity
- soft hyperconnectedness
- soft almost Lindelofness
MSC
References
-
[1]
S. Al Ghour, Strong form of soft semiopen sets in soft topological spaces, Int. J. Fuzzy Log. Intell. Syst., 21 (2021), 159–168
-
[2]
S. Al Ghour, On soft generalized !-closed sets and soft T1=2 spaces in soft topological spaces, Axioms, 11 (2022), 1–12
-
[3]
S. Al Ghour, Soft regular generalized !-closed sets and soft !-T1=2 spaces, Axioms, 11 (2022), 1–13
-
[4]
S. Al Ghour, Soft !-regular open sets and soft nearly Lindel¨ofness, Heliyon, 8 (2022), 1–8
-
[5]
S. Al Ghour, Somewhat omega continuity and somewhat omega openness in soft topological spaces, J. Intell. Fuzzy Syst., 44 (2023), 1385–1396
-
[6]
S. Al Ghour, A. Bin-Saadon, On some generated soft topological spaces and soft homogeneity, Heliyon, 5 (2019), 10 pages
-
[7]
S. Al Ghour, W. Hamed, On two classes of soft sets in soft topological spaces, Symmetry, 12 (2020), 1–22
-
[8]
H. H. Al-jarrah, A. Rawshdeh, T. M. Al-shami, On soft compact and soft Lindelof spaces via soft regular closed sets, Afr. Mat., 33 (2022), 1–16
-
[9]
T. M. Al-shami, Defining and investigating new soft ordered maps by using soft semi open sets, Acta Univ. Sapientiae Math., 13 (2021), 145–163
-
[10]
T. M. Al-shami, On soft separation axioms and their applications on decision-making problem, Math. Probl. Eng., 2021 (2021), 12 pages
-
[11]
T. M. Al-shami, Compactness on soft topological ordered spaces and its application on the information system, J. Math., 2021 (2021), 12 pages
-
[12]
T. M. Al-shami, A. Mhemdi, Two families of separation axioms on infra soft topological spaces, Filomat, 36 (2022), 1143–1157
-
[13]
T. M. Al-shami, M.E. El-Shafei, M. Abo-Elhamayel, Almost soft compact and approximately soft Lindel¨of spaces, J. Taibah Univ. Sci., 12 (2018), 620–630
-
[14]
T. M. Al-shami, Z. A. Ameen, A. A. Azzam, M. E. El-Shafei, Soft separation axioms via soft topological operators, AIMS Math., 7 (2022), 15107–15119
-
[15]
T. M. Al-shami, A. Mhemdi, R. Abu-Gdairi, M. E. El-Shafei, Compactness and connectedness via the class of soft somewhat open sets, AIMS Math., 8 (2023), 815–840
-
[16]
T. M. Al-shami, A. Mhemdi, A. A. Rawshdeh, H. H. Al-jarrah, Soft version of compact and Lindelof spaces using soft somewhere dense set, AIMS Math., 6 (2021), 8064–8077
-
[17]
Z. A. Ameen, A non-continuous soft mapping that preserves some structural soft sets, J. Intell. Fuzzy Syst., 42 (2022), 5839–5845
-
[18]
B. A. Asaad, Results on soft extremally disconnectedness of soft topological spaces, J. Math. Comput. Sci., 17 (2017), 448–464
-
[19]
A. Ayg¨uno˘ glu, H. Ayg¨ un, Some notes on soft topological spaces, Neural Comput. Appl., 21 (2012), 113–119
-
[20]
A. A. Azzam, Z. A. Ameen, T. M. Al-shami, M. E. El-Shafei, Generating Soft Topologies via Soft Set Operators, Symmetry, 14 (2022), 13 pages
-
[21]
H. M. Darwesh, H. A. Shareef, !-topology, Ital. J. Pure Appl. Math., 47 (2022), 413–422
-
[22]
D. N. Georgiou, A. C. Megaritis, V. I. Petropoulos, On soft topological spaces, Appl. Math. Inf. Sci., 7 (2013), 1889– 1901
-
[23]
S. Hussain, B. Ahmad, Soft separation axioms in soft topological spaces, Hacet. J. Math. Stat., 44 (2015), 559–568
-
[24]
C. Kuratowski, Sur l’op´eration ¯A de l’Analysis Situs, Fundam. Math., 3 (1922), 182–199
-
[25]
A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh, A. M. A. Abd El-latif, Soft connectedness via soft ideals, J. New Results Sci., 4 (2014), 90–108
-
[26]
Y. Lei, J. Zhang, Generalizing topological set operators, Electron. Notes Theor. Comput. Sci., 345 (2019), 63–76
-
[27]
D. Molodtsov, Soft set theory—First results, Comput. Math. Appl., 37 (1999), 19–31
-
[28]
S. Y. Musa, B. A. Asaad, Hypersoft topological spaces, Neutrosophic Sets Syst., 49 (2022), 397–415
-
[29]
Z. Pawlak, Rough sets, Int. J. Comput. Inf. Sci., 11 (1982), 341–356
-
[30]
M. E. Sayed, M. K. El-Bably, Soft simply open sets in soft topological space, J. Comput. Theor. Nanosci., 14 (2017), 4100–4103
-
[31]
M. Shabir, M. Naz, On soft topological spaces, Comput. Math. Appl., 61 (2011), 1786–1799
-
[32]
L. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353
