FUZZY STRONGLY IRRESOLVABLE SPACES AND FUZZY SIMPLY OPEN SETS
Keywords:
fuzzy dense set, fuzzy nowhere dense set, fuzzy simply* open set, fuzzy hyperconnected space, fuzzy globally disconnected space, fuzzy submaximal space, fuzzy irresolvable space, fuzzy P-space.DOI:
https://doi.org/10.17654/0973421X22001Abstract
In this paper, fuzzy strongly irresolvability of fuzzy topological space is established by means of fuzzy simply open sets. It is established that fuzzy hyperconnected spaces are fuzzy strongly irresolvable spaces whereas fuzzy perfectly disconnected spaces are not necessarily fuzzy strongly irresolvable spaces. The conditions under which fuzzy Moscow spaces and fuzzy P-spaces become fuzzy strongly irresolvable spaces are obtained. It is established that fuzzy P-spaces with fuzzy strongly irresolvability and fuzzy nodefness are fuzzy submaximal spaces. The condition under which a fuzzy strongly irresolvable space becomes a fuzzy Baire space is also obtained by means of fuzzy resolvable sets.
Received: October 1, 2021
Accepted: November 10, 2021
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.
G. Balasubramanian, Fuzzy β-open sets and fuzzy β-separation axioms, Kybernetika 35(2) (1999), 215-223.
R. Bolstein, Sets of points of discontinuity, Proc. Amer. Math. Soc. 38 (1973), 193-197.
A. S. Bin Shahna, On fuzzy strong semi continuity and fuzzy pre continuity, Fuzzy Sets and Systems 44 (1991), 303-308.
B. Chacko, Some lattice theoretic problems related to set topology and fuzzy topology, Ph.D. Thesis submitted to University of Calicut, Kerala, India, 2008.
C. L. Chang, Fuzzy topological spaces, J. Math. Anal. 24 (1968), 182-190.
A. G. El’kin, Ultrafilters and undecomposable spaces, Vestnik Mosk. Univ. Mat. 24(5) (1969), 51-56.
M. A. Fath Alla, On fuzzy topological spaces, Ph.D. Thesis, Assiut. Univ. Sohag, Egypt, 1984.
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 21(1) (2002), 51-63.
P. M. Pu and Y. M. Liu, Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76(2) (1980), 571-599.
R. Palani, Contributions to the study on some aspects of fuzzy Baire spaces, Ph.D. Thesis, Thiruvalluvar University, Tamilnadu, India, 2017.
D. Rose, K. Sizemore and B. Thurston, Strongly irresolvable spaces, Inter. J. Math. Math. Sci., Vol. 2006, Article ID: 53653, pp. 1-12.
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 and G. Balasubramanian, On fuzzy resolvable and fuzzy irresolvable spaces, Fuzzy Sets, Rough Sets and Multivalued Oper. 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 and K. Dinakaran, On fuzzy simply* continuous functions, Adv. Fuzzy Math. 11(2) (2016), 245-264.
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. Muruganantham, On fuzzy perfectly disconnected spaces, Int. J. Adv. Math. 5 (2017), 12-21.
G. Thangaraj and S. Muruganantham, On fuzzy globally disconnected spaces, J. Tripura Math. Soc. 21 (2019), 37-46.
G. Thangaraj and S. Lokeswari, Fuzzy irresolvable sets and fuzzy open hereditarily irresolvable spaces, Bull. Pure Appl. Sci. 38(1) (2019), 369-377.
G. Thangaraj and S. Lokeswari, A note on fuzzy resolvable sets, J. Fuzzy Math. 27(4) (2019), 925-938.
G. Thangaraj and J. Premkumar, On fuzzy -spaces, Adv. Fuzzy Math. 14(1) (2019), 27-40.
G. Thangaraj and M. Raji, Fuzzy sets having the fuzzy Baire property, Ann. Fuzzy Math. Inform. 21(2) (2021), 147-160.
G. Thangaraj and A. Vinothkumar, On fuzzy Moscow spaces (Communicated to Annals of Fuzzy Mathematics and Informatics).
G. Thangaraj and V. Seenivasan, On fuzzy strongly irresolvable spaces, Proc. Nat. Conf. on Fuzzy Math. Graph Theory, Jamal Mohamed College, Trichy, Tamilnadu, India, 2008.
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.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 Pushpa Publishing House, Prayagraj, India
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
Citation count: 
Google h-index: 
Downloads: 