α-b-regularity in a fuzzy topological space
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This paper deals with a new type of fuzzy separation axiom, viz., fuzzy α-b-regular space by introducing fuzzy α-b-open set as a basic tool. This newly defined class of sets is strictly larger than that of fuzzy open set as well as fuzzy preopen set, fuzzy semiopen set, fuzzy α-open set and fuzzy β-open set. Also, we introduce new type of fuzzy compact space and a strong form of fuzzy T2-space. However, three different types of functions are introduced and studied. Also the mutual relationships of these functions are established. Lastly some applications of these functions on the spaces introduced here are established.
Abstract
This paper deals with a new type of fuzzy separation axiom, viz., fuzzy α-b-regular space by introducing fuzzy α-b-open set as a basic tool. This newly defined class of sets is strictly larger than that of fuzzy open set as well as fuzzy preopen set, fuzzy semiopen set, fuzzy α-open set and fuzzy β-open set. Also, we introduce new type of fuzzy compact space and a strong form of fuzzy T2-space. However, three different types of functions are introduced and studied. Also the mutual relationships of these functions are established. Lastly some applications of these functions on the spaces introduced here are established.
참고문헌 (20)
- A. S. Bin Shahna, "On fuzzy strong semicontinuity and fuzzy precontinuity", Fuzzy Sets and Systems, 44, pp.303~308 (1991)
- C. L. Chang, "Fuzzy topological spaces", J. Math. Anal. Appl, 24, pp.182~190 (1968)
- K. K. Azad, "On fuzzy semi-continuity, fuzzy almost continuity and fuzzy weakly continuity", J. Math. Anal. Appl, 82, pp.14~32 (1981)
- B. Hutton, "Separation axioms in fuzzy topological spaces", Fuzzy sets and Systems, 31, pp.93~104 (1980)
- J. G. Lee, "Octahedron sets", Ann. Fuzzy Math. Inform, 19(3), pp.211~238 (2020)
- G. S¸enel, "Soft closed sets on soft bitopological space", Journal of New Results in Science, 3(5), pp.57~66 (2014)
- G. S¸enel, "Soft topological subspaces", Ann. Fuzzy Math. Inform, 10(4), pp.525~535 (2015)
- G. S¸enel, "A new approach to Hausdorff space theory via the soft sets", Mathematical Problems in Engineering, pp.1~6[DOI]
- G. S¸enel, "Soft topology generated by L-Soft sets", Journal of New Theory, 24(4), pp.88~100 (2018)
- G. S¸enel, "Distance and similarity measures for octahedron sets and their applications to MCGDM problems", Mathematics, 8, pp.16~90 (2020)
- L. A. Zadeh, "Fuzzy Sets", Information and Control, 8, pp.338~353 (1965)
- Pao Ming Pu, "Fuzzy topology I. Neighbourhood structure of a fuzzy point and Moore-Smith Convergence", J. Math Anal. Appl, 76, pp.571~599 (1980)
- S. Nanda, "Strongly compact fuzzy topological spaces", Fuzzy Sets and Systems, 42, pp.259~262 (1991)
- M. A. Fath Alla, "On fuzzy topological spaces", Ph.D., pp.1984
- Anjana Bhattacharyya, "Concerning almost quasi continuous fuzzy multifunctions", Universitatea Din Bacˇau Studii S. i Cercetˇari, S. tiintifice Seria : Matematicˇa, 11, pp.35~48 (2001)
- Anjana Bhattacharyya, "Several concepts of continuity in fuzzy setting", The 10th International Conference MSAST 2016, pp.282~293 (2016)
- M. N. Mukherjee, "On nearly compact and θ-rigid fuzzy sets in fuzzy topological spaces", Fuzzy Sets and Systems, 43, pp.57~68 (1991)
- S. Ganguly, "A note on compactness in fuzzy setting", Fuzzy Sets and Systems, 34, pp.117~124 (1990)
- S. P. Sinha, "On s-closed fuzzy topological spaces", J. Fuzzy Math, 2(1), pp.95~103 (1994)
- C. K. Wong, "Fuzzy points and local properties of fuzzy topology", J. Math. Anal. Appl, 46, pp.316~328 (1974)