ON FUZZY $\partial^*$ SPACES
Keywords:
fuzzy $G_\delta$-set, fuzzy $F_\sigma$-set, fuzzy nowhere dense set, fuzzy residual set, fuzzy simply* open set, fuzzy hyperconnected space, fuzzy $P$-space, fuzzy weakly Baire space.DOI:
https://doi.org/10.17654/0973421X22009Abstract
In this paper, a new class of fuzzy topological spaces, namely, fuzzy $\partial^*$ spaces, is introduced and studied. It is obtained that fuzzy $G_\delta$-sets are fuzzy somewhere dense sets but not fuzzy simply open sets, and fuzzy $F_\sigma$-sets are fuzzy $c s$ dense sets but not fuzzy dense sets. Fuzzy $\sigma$-nowhere dense sets and fuzzy $\sigma$-boundary sets are fuzzy simply* closed sets in fuzzy $\partial^*$ spaces. The conditions under which a fuzzy $\partial^*$ space becomes a fuzzy weakly Baire space, and a fuzzy $P$-space becomes a fuzzy $\partial^*$ space are also obtained.
Received: January 13, 2022
Accepted: May 9, 2022
References
K. K. Azad, On fuzzy semi continuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl. 82 (1981), 14-32.
F. Azarpanah and M. Karavan, On nonregular ideals and $z^o$-ideals in Czech. Math. J. 55(2) (2005), 397-407.
G. Balasubramanian, Maximal fuzzy topologies, Kybernetika 31(5) (1995), 459-464.
C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182-190.
Miguel Caldas, Govindappa Navalagi and Ratnesh Saraf, On fuzzy weakly semiopen functions, Proyecciones 21(1) (2002), 51-63.
G. Thangaraj and G. Balasubramanian, On fuzzy basically disconnected spaces, J. Fuzzy Math. 9(1) (2001), 103-110.
G. Thangaraj and G. Balasubramanian, On somewhat fuzzy continuous functions, J. Fuzzy Math. 11(2) (2003), 725-736.
G. Thangaraj, Resolvability and irresolvability in fuzzy topological spaces, News Bull. Calcutta Math. Soc. 31(4-6) (2008), 11-14.
G. Thangaraj and S. Anjalmose, On fuzzy Baire spaces, J. Fuzzy Math. 21(3) (2013), 667-676.
G. Thangaraj and E. Poongothai, On fuzzy σ-Baire spaces, Int. J. Fuzzy Math. Sys. 3(4) (2013), 275-283.
G. Thangaraj and C. Anbazhagan, On fuzzy almost P-spaces, Inter. J. Innov. Sci. Engin. & Tech. 2(4) (2015), 389-407.
G. Thangaraj and K. Dinakaran, On fuzzy simply continuous functions, J. Fuzzy Math. 25(1) (2017), 99-124.
G. Thangaraj and K. Dinakaran, On fuzzy simply* continuous functions, Inter. J. Advances in Math. 2017(5) (2017), 12-21.
G. Thangaraj and R. Palani, On fuzzy weakly Baire spaces, Bull. Inter. Math Virtual Institute 7 (2017), 479-489.
G. Thangaraj and J. Premkumar, On fuzzy ∂-spaces, Inter. J. Appl. Engin. Research 13(15) (2018), 12417-12421.
G. Thangaraj and S. Senthil, On somewhere fuzzy continuous functions, Ann. Fuzzy Math. Inform. 15(2) (2018), 181-198.
G. Thangaraj and S. Muruganantham, On fuzzy globally disconnected spaces, J. Tri. Math. Soc. 21 (2019), 37-46.
G. Thangaraj and S. Logeshwari, Fuzzy strongly irresolvable spaces and fuzzy simply open sets, Adv. Fuzzy Sets & Sys. 27(1) (2022), 1-34.
L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353.
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