F-Closedness in Bitopological Spaces

Subject Areas : History and biography

A. A. Nasef ¹ , A. Azzam ²

1 - Department of Physics and Engineering Mathematics, Faculty of Engineering, KafrEl-Sheikh University, Kafr El-Sheikh, Egypt
2 - Department of Mathematics, Faculty of Science, Assuit University, New Valley, Egypt

Received: 2016-02-20 Accepted : 2016-05-10 Published : 2016-06-01

Keywords: pairwise S-closed, pairwise quasi H-closed, pairwise almost co-compact, pairwise strongly compact, F-closed, pairwise F-closed,

Abstract :

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.

References:

[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.