ON FUZZY HEREDITARILY IRRESOLVABLE SPACES
Keywords:
fuzzy dense set, fuzzy nowhere dense set, fuzzy simply open set, fuzzy hyperconnected space, fuzzy perfectly disconnected space, fuzzy submaximal space, fuzzy irresolvable space, fuzzy Baire space.DOI:
https://doi.org/10.17654/0973421X22004Abstract
In this paper, fuzzy hereditarily irresolvablity of a fuzzy topological space is established by means of closures of fuzzy sets. It is found that a fuzzy hyperconnected space is not a fuzzy perfectly disconnected space, while a fuzzy perfectly disconnected space is a fuzzy hereditarily irresolvable space. It is obtained that fuzzy hereditarily irresolvablity and fuzzy strongly irresolvablity of a fuzzy topological space are independent notions. Furthermore, it is established that the existence of fuzzy nowhere dense sets and fuzzy simply open sets ensures the non-hereditarily irresolvablity of a fuzzy topological space.
Received: November 23, 2021
Accepted: February 8, 2022
References
K. K. Azad, On fuzzy semi continuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl. 82 (1981), 14-32.
G. Balasubramanian, Maximal fuzzy topologies, Kybernetika 31(5) (1995), 459-464.
C. L. Chang, Fuzzy topological spaces, J. Math. Anal. 24 (1968), 182-190.
J. Foran and P. Liebnitz, A characterization of almost resolvable spaces, Rend. Circ. Mat. Palermo (2) 40(1) (1991), 136-141.
B. Ghosh, Fuzzy extremally disconnected spaces, Fuzzy Sets and Systems 46(2) (1992), 245-250.
E. Hewitt, A problem of set theoretic topology, Duke Math. J. 10 (1943), 309-333.
M. Katetov, On topological spaces containing no disjoint dense sets, Mat. Sb. 21 (1947), 3-12.
Miguel Caldas, Govindappa Navalagi and Ratnesh Saraf, On fuzzy weakly semi-open functions, Proyecciones, Universidad Catolica del Norte, Antofagasta – Chile 21(1) (2002), 51-63.
G. Thangaraj and G. Balasubramanian, On somewhat fuzzy continuous functions, J. Fuzzy Math. 11(2) (2003), 725-736.
G. Thangaraj and G. Balasubramanian, On fuzzy resolvable and fuzzy irresolvable spaces, Fuzzy Sets, Rough Sets and Multivalued Operations and Appl. 1(2) (2009), 173-180.
G. Thangaraj and S. Anjalmose, On fuzzy baire spaces, J. Fuzzy Math. 21(3) (2013), 667-676.
G. Thangaraj and K. Dinakaran, On fuzzy simply continuous functions, J. Fuzzy Math. 25(1) (2017), 99-124.
G. Thangaraj, B. Mathivathani and P. Sathya, On fuzzy resolvable sets and fuzzy resolvable functions, Adv. Fuzzy Math. 12(6) (2017), 1171-1181.
G. Thangaraj and S. Lokeswari, Fuzzy irresolvable sets and fuzzy open hereditarily irresolvable spaces, Bull. Pure and Appl. Sci. 38(1) (2019), 369-377.
G. Thangaraj and S. Lokeswari, Fuzzy strongly irresolvable spaces and fuzzy simply open sets, Adv. Fuzzy Sets and Sys. 27(1) (2022), 1-33.
G. Thangaraj and S. Muruganantham, On fuzzy perfectly disconnected spaces, Inter. J. Adv. Math. 5 (2017), 12-21.
R. H. Warren, Boundary of a fuzzy set, Indiana J. Math. 26 (1977), 191-197.
L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353.
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