F-Closedness in Bitopological Spaces
محورهای موضوعی : History and biography
A. A. Nasef
1
(Department of Physics and Engineering Mathematics, Faculty of Engineering, KafrEl-Sheikh University, Kafr El-Sheikh, Egypt)
A. Azzam
2
(Department of Mathematics, Faculty of Science, Assuit University,
New Valley, Egypt)
کلید واژه: pairwise S-closed, pairwise quasi H-closed, pairwise almost co-compact, pairwise strongly compact, F-closed, pairwise F-closed,
چکیده مقاله :
The purpose of this paper is to introduce the concept of pairwise F-closedness in bitopological spaces. This space contains both of pairwise strongcompactness and pairwise S-closedness and contained in pairwise quasi H-closedness. The characteristics and relationships concerning this new class of spaces with other corresponding types are established. Moreover, several of its basic and important properties are discussed.
[1] G. K. Banerjee, On Pairwise Almost Strongly θ-continuous mappings, Bull. Cal. Math. Soc. 79 (1987), 314- 320.
[2] V. R. Caroll, H-closure for bitopological spaces, Kyungpook Math. J. 18 (2) (1978), 159-165.
[3] G. I. Chae, D. W. Lee and H. W. Lee, Feebly irresolute functions, Sung Shin W. Univ. Report, 21 (1985), 273-280.
[4] G. I. Chae and D. W. Lee, F-closed spaces, Kyungpook Math. J. 27 (2) (1987), 127-134.
[5] G. Di. Maio, Bitopological H-closedness and S-closedness, Rend. Circ. Mat. Palermo(2) Supp1. No. 12(1986), 231-243.
[6] P. Flether, H. B. Hoyle and W. C. Patty, The comparison of topologies, Duke Math. J., 36 (1969) 325-331.
[7] M. Ganster and A. Kanibir, On Pairwise S-closed spaces, R and A in General topology, Vol. 15(1997), 129-136.
[8] M. Jelic, A decomposition of pairwise continuity, J. Inst. Math. and Comp. Sci. (Math. Ser.), 3(1990), 25-29.
[9] M. Jelic, Feebly p-continuous mappings, Suppl. Rend. Circ. Mat. Palermo(2). 24 (1990), 387-397.
[10] J. C. Kelly, Bitopological spaces, Proc. London Math. Soc., 3 (13) (1963), 71-89.
[11] F. H. Khedr, Properties of pairwise S-closed spaces, Delta J. Sci., 8 (1984), 1-8.
[12] F. H. Khedr, T. Noiri, On pairwise S-closed spaces, Inst, Math. and Comp. Sci., 4 (1991), 367-371.
[13] Y. W. Kim, Pairwise compactness, Pub. Math. Debrecea 15 (1968), 87-90.
[14] S. S. Kumar, Pairwise α-open, α-closed and α-irresolute functions in bitopological spaces, Bull. Inst. Math. Acad. Sinice 21 (1993), 59-72.
[15] S. N. Maheshwari, R. Prasad, Semi-open sets and semi-continuous function in bitopological spaces, Math. Notae, 26 (1977/78), 29-37.
[16] S. N. Maheshwari, U. D. Tapi, Note on some applications of feebly open sets, M. B. J. Univ. of Saugar, (1979).
[17] A. S. Mashhour, F. H. Khedr, I. A. Hasanein and A. A. Allam, S-closedness in bitopological spaces, Ann. Soc. Sci. Bruxelles, 96 (1982), 69-76.
[18] M. N. Mukherjee, On pairwise S-closed bitopological spaces, Internat. J. Math. and Math. Sci. 8(4) (1985), 729-745.
[19] T. Noiri, A note on F-closed spaces, Kyungpook Math. J. 31 (2) (1991), 269-273.
[20] T. Noiri, A. S. Mashhour, F. H. Khedr and I. A. Hasanein, Strong-compactness in bitopological spaces, Indian J. Math. 25 (1) (1983), 33-39.
[21] J. Porter, J. Thomas, On H-closed and minimal Hausdroff spaces. Trans. Amer. Math. Soc. 138 (1969), 159-170
[22] M. K. Singal, S. P. Arya, On almost-regular spaces, Glasnik Mat. 4 (1969), 89-99.
[23] M. K. Singal, A. Mathur, On nearly-compact spaces, Boll. Un-Mat-Ital. 4 (2) (1969), 702-710.
[24] M. K. Singal, A. R. Singal, Some more separation axioms in bitopological spaces, Ann. Soc. Sci. Bruxelles 84 (1970), 207-230.
[25] T. Thompson, S-closed spaces, Proc. Amer. Math. Soc. 60 (1976), 335-338.
