On Fuzzy Weakly-Closed Sets

A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets. Alongwith the study of fundamental results of such closed sets, we define and characterize fuzzy weakly compact space and fuzzy weakly closed space.

• J. Mahanta
• P.K. Das

• Fuzzy weakly-closed set
• fuzzy weakly-closed space
• fuzzy weakly-compactness
• MSC: 54A40
• 54D30.

<p>[1] Arya, S.P., Nour, T., Characterization of s-normal spaces, Indian J. Pure
Appl. Math., 21, (1990), 717–719.
[2] Azad, K. K., On fuzzy semicontinuity, fuzzy almost continuity and fuzzy
weakly continuity, J. Math. Anal. Appl., 82, (1981), 14–32.
[3] Balasubramanian, G., Sundaram, P., On some generalizations of fuzzy
continuous functions, Fuzzy Sets and Systems, 86, (1997), 93–100.
[4] Benchalli, S.S., Wali, R.S., On Rw-closed sets in topological spaces,
Bull. Malays. Math. Sci. Soc., 30(2), (2007), 99–110.
[5] Bhattacharyya, P., Lahiri, B.K., Semi generalized closed sets in topology,
Indian J. Pure Appl. Math., 29, (1987), 375–382.
[6] Bin Shahna, A.S., On fuzzy strong semi-continuity and fuzzy precontinuity,
Fuzzy Sets and Systems, 44, (1991), 14–32.
[7] Caldas, M., Navagi, G., Saraf, R., On some functions concerning fuzzy
pg-closed sets, Proyecciones, 25(3), (2006), 262–271.
[8] Chang, C.L., Fuzzy topological spaces, J. Math. Anal. Appl. 24, (1968),
182-190.
[9] El-Shafei, M.E., Zakari, A., Semi-generalized continuous mappings in
fuzzy topological spaces, J. Egyptian Math. Soc. 15(1), (2007), 57-67.
[10] Ganguly, S., Saha, S., A note on compactness in fuzzy setting, Fuzzy
Sets and Systems, 34, (1990), 117–124.
[11] Livine, N., Semiopen sets and continuity in topological spaces, Amer.
Math. Monthly, 70, (1963), 36–41.
[12] Livine, N., Generalized closed sets in topology, Rend. Circ. Mat.
Palemore, 19, (1970), 89–96.
[13] Lowen, R., Fuzzy topological spaces and fuzzy compactness, J. Math.
Anal. Appl., 56, (1976), 621–633.
[14] Mahanta, J., Das, P.K., On fuzzy g*s-closed sets, International Journal
of Computer Applications, 43:2, (2012), 17-21.
[15] Maki, H., Fukutake, T., Kojima, M., Harada, H., Generalized closed sets
in fuzzy topological spaces,I, Meeting on Topological Spaces, Theory
and its Applications, (1998), 23–36.
[16] Maki, H., Devi, R., Balachandran. K., Generalized α-closed sets in
topology, Bull. Fukuoka Univ. Ed. Part-III, 42, (1993), 13–21.
[17] Navalagi, G.B., Definition bank in general topology, Topology Atlas
Preprint # 449, May, 2000.
[18] Palaniappan, N., Fuzzy Topology, Narosa Publishing House, 2002.
[19] Saraf, R.K., Caldas, M., Mishra, S., Results via Fgα−closed sets and
Fαg-closed sets, preprint.
[20] Saraf, R.K., Navalagi, G., Kumar, M., On fuzzy semi-pre-generalized
closed sets, Bull. Mal. Mat. Sci. Soc,, 28(1), (2005), 19–30.
[21] Sundaram, P., Sheik John, M., On w-closed sets in topology, Acta
Ciencia Indica, 4, (2000), 389–392.
[22] Thakur, S.S., Singh, S., On fuzzy semi-preopen sets and fuzzy semi-pre
continuity, Fuzzy Sets and Systems,, 98, (1998), 383–391.</p>