\(\theta_s\)-open sets and \(\theta_{s}\)-continuity of maps in the product space
-
1301
Downloads
-
1981
Views
Authors
Javier A. Hassan
- Department of Mathematics \(\&\) Statistics, College of Science \(\&\) Mathematics, Mindanao State University-Iligan Institute of Technology, Iligan City, Philippines.
Mhelmar A. Labendia
- Department of Mathematics \(\&\) Statistics, College of Science \(\&\) Mathematics, Mindanao State University-Iligan Institute of Technology, Iligan City, Philippines.
Abstract
In this study, the concept of \(\theta_s\)-open set is introduced. The topology formed by \(\theta_s\)-open sets is strictly finer than the topology formed by \(\theta\)-open sets but is not comparable with the topology formed by \(\omega_\theta\)-open sets. Related concepts such as \(\theta_s\)-open and \(\theta_s\)-closed functions, \(\theta_s\)-continuous function, \(\theta_s\)-connected space, and some versions of separation axioms are defined and characterized. Finally, the concept of \(\theta_s\)-continuous function from an arbitrary topological space into the product space is investigated further.
Share and Cite
ISRP Style
Javier A. Hassan, Mhelmar A. Labendia, \(\theta_s\)-open sets and \(\theta_{s}\)-continuity of maps in the product space, Journal of Mathematics and Computer Science, 25 (2022), no. 2, 182--190
AMA Style
Hassan Javier A., Labendia Mhelmar A., \(\theta_s\)-open sets and \(\theta_{s}\)-continuity of maps in the product space. J Math Comput SCI-JM. (2022); 25(2):182--190
Chicago/Turabian Style
Hassan, Javier A., Labendia, Mhelmar A.. "\(\theta_s\)-open sets and \(\theta_{s}\)-continuity of maps in the product space." Journal of Mathematics and Computer Science, 25, no. 2 (2022): 182--190
Keywords
- \(\theta_s\)-open
- \(\theta_s\)-closed
- \(\theta_s\)-connected
- \(\theta_s\)-continuous
- \(\theta_s\)-Hausdorff
- (\theta_s\)-regular
- \(\theta_s\)-normal
MSC
References
-
[1]
T. A. Al-Hawary, On supper continuity of topological spaces, MATEMATIKA: Malays. J. Indust. Appl. Math., 21 (2005), 43--49
-
[2]
H. H. Aljarrah, M. S. M. Noorani, T. Noiri, Contra $\omega\beta$-continuity, Bol. Soc. Parana. Mat. (3), 32 (2014), 9--22
-
[3]
H. H. Aljarrah, M. S. M. Noorani, T. Noiri, On generalized $\omega\beta$-closed sets, Missouri J. Math. Sci., 26 (2014), 70--87
-
[4]
K. Al-Zoubi, K. Al-Nashef, The topology of $\omega$-open subsets, Al-Manarah Journal, 9 (2003), 169--179
-
[5]
M. Caldas, S. Jafari, M. M. Kovar, Some properties of $\theta$-open sets, Divulg. Mat., 12 (2004), 161--169
-
[6]
M. Caldas, S. Jafari, R. M. Latif, Sobriety via $\theta$-open sets, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 56 (2010), 163--167
-
[7]
C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Properties of faintly $\omega$-continuous functions, Bol. Mat., 20 (2013), 135--143
-
[8]
C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Some properties of upper/lower $\omega$-continuous multifunctions, Sci. Stud. Res. Ser. Math. Inform., 23 (2013), 35--55
-
[9]
C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, On upper and lower almost contra-$\omega$-continuous multifunctions, Ital. J. Pure Appl. Math., 32 (2014), 445--460
-
[10]
C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Somewhat $\omega$-continuous functions, Sarajevo J. Math., 11 (2015), 131--137
-
[11]
C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Upper and lower $\omega$-continuous multifunctions, Afr. Mat., 26 (2015), 399--405
-
[12]
H. M. Darwesh, Between preopen and open sets in topological spaces, Thai J. Math., 11 (2013), 143--155
-
[13]
R. F. Dickman, J. R. Porter, $\theta$-closed subsets of Hausdorff spaces, Pacific J. Math., 59 (1975), 407--415
-
[14]
R. F. Dickman, J. R. Porter, $\theta$-perfect and $\theta$-absolutely closed functions, Illinois J. Math., 21 (1977), 42--60
-
[15]
E. Ekici, S. Jafari, R. M. Latif, On a finer topological space than $\tau_\theta$ and some maps, Ital. J. Pure Appl. Math., 27 (2010), 293--304
-
[16]
H. Z. Hdeib, $\omega$-closed mappings, Rev. Colombiana Mat., 16 (1982), 65--78
-
[17]
D. S. Jankovic, $\theta$-regular spaces, Internat. J. Math. Math. Sci., 8 (1986), 615--619
-
[18]
J. E. Joseph, $\theta$-closure and $\theta$-subclosed graphs, Math. Chronicle, 8 (1979), 99--117
-
[19]
M. M. Kovár, On $\theta$-regular spaces, Internat. J. Math. Math. Sci., 17 (1994), 687--692
-
[20]
M. A. Labendia, J. A. C. Sasam, On $\omega$-connectedness and $\omega$-continuity in the product space, Eur. J. Pure Appl. Math., 11 (2018), 834--843
-
[21]
N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36--41
-
[22]
P. E. Long, L. L. Herrington, The $\tau_\theta$-topology and faintly continuous functions, Kyungpook Math. J., 22 (1982), 7--14
-
[23]
T. Noiri, S. Jafari, Properties of $(\theta,s)$-continuous functions, Topology Appl., 123 (2002), 167--179
-
[24]
N. Veličko, $H$-closed topological spaces, (Russian) Mat. Sb. (N.S.), 70 (1966), 98--112