S-COMPACTNESS VIA IDEALS

Authors

  • M. E. ABD EL-MONSEF Tanta University, Tanta, Egypt.
  • E. F. LASHIEN Tanta University, Tanta, Egypt.
  • A. A. NASEF Tanta University, Tanta, Egypt.

DOI:

https://doi.org/10.5556/j.tkjm.24.1993.4515

Keywords:

I-compact, countably I-compact, SI-compact, countably SI­ compact

Abstract

Compactness modulo an ideal has not been widely studied. Many new sorts of weak compactness have been introduced to topological spaces in the last twenty years but have not been studied using ideals. So, the main aim of our work is to study relations between ideals and some types of weak compactness. We initiate types of compactness modulo an ideal that generalize semi-compactness, $S$-closeness, $S$-Lindelofness and other types of compactness. Moreover, we study some of their properties and characterizations.

References

M. E. Abd El-Monsef; S. N. El-Deeb and R. A. Mahmoud, "beta-open sets and beta-continuous mapprngs", Bull. Fae. Sci., Assiut Univ., 12 (1) (1983), 77-90.

M. E. Abd El'."Monsef; I. A. Hasanein; A. S. Mashhour and T. Noiri, "Strongly compact spaces", Delta J. Sci., (8) (1984), 30-46.

M. E. Abd El-Monsef and A. M. Kozae, "Some generalized forms of compactness and closedness", Delta J. Sci., (9) (2) (1985), 257-269.

----, "On extremally disconnectedness ro-equivlence and properties of some maximal topologies", Proc. 4th Conf. Oper. Res. and Math. Method, Alex. Univ., (1988).

M. E. Abd El-Monsef and E. F. Lashien, "On Simple Extensions of topologies", Journal of the Fae. of Edu., Ain Shams Univ., Fifth Top. Symp., NQ. 12 (1987), 71-82.

M. E. Abd El-Monsef and E. F. Lashien, "Filter Extensions of Topologies", accepted for publication in Proc. 3rd Conf. Math. Stat. 0. R. and Appl. Bull. Fae. of Sci., Alex. Univ.

M. E. Abd El-Monsef, E. F. Lashien and A. A. Nasef, "Some Topological Operators Via Ideals", to appear in the First International Conference on Topology and Its Applications in 1990.

R. W. Bagley, E. H. Connell, and J. D. McKnight, "On properties charactrizing pseudo compact spaces", Proc. Amer. Math. Soc., 9 (1958), 500-506.

N. Bourbaki, "General Topology", Addison- Wesley, Mass., I966.

D. E. Cameron, "Properties of S-closed spaces", Proc. Amer. Math. Soc., V. (72), (3) (1978), 581-586.

D. Carnahan, "Locally nearly-compact spaces", Bull. Un. Math. Ital., (4) 6 (1972), 146-153.

S. G. Grossley and S. K. Hildebrand, "Semi-closure", Texas J. Sci.,·22 (2+3) (1971), 99-112.

----, "Semi-Topological properties", Fund. Math., 14 {1972), 233-254.

G. Di Maio, "S-closed spaces, S-sets and S-continuous functions", Atti-Accad. Sci. Torino, 118 (1984), 125-134.

G. Di Maio and T. Noiri, "On s-closed spaces", Indian J. Pure Appl. Math., 18 (3) (1987), 226-233.

C. Dorsett, "Semi convergence and semi-compactness", Indian J. Math. Mech., 19 (1981), 11-17.

T. R. Hamlett and D. Jankovic, "Compactness with respect to an ideal", Boll. U. M. I., (7), 4-B (1990), 849-861.

T. R. Hamlett, D. Jankovic and D. Rose, "Countable compactness with respect to an ideal Math", Chron., 20 (1991), 109-126.

E. Hewitt, "A problem of set theoretic topology", Duke Math. J., 10 (1943), 309-333.

K. Kuratowski, "Topologies I", Warszawa, 1993.

N. Levine, "Semi-open sets and semi-continuity in topological spaces", Amer. Math. Monthly, 70 (1963), 36-41.

N. Levine, "Simple extensions of topologies", Amer. Math. Monthly, 71 (1964), 22-25.

R. A. Mahmoud and M. E. Abd El-Monsef, "beta-Irresolute and beta-Topological invariant", accepted in Pakistan Academy of Sciences in 1990.

A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, "On precontinuous and weak precontinuous mappings", Proc. Math. Phys. Soc., Egypt. (53) (1982), 47-53.

A. S. Mashhour, I. A. Hasanein and S. N. El-Deeb, "a-continuous and a-open mappings", Acta, Math. Acad. Sci. Hungar, (3+ 4) (1983), 213-218.

J. Mioduszewski and L. Rudolf, "H-closed and extremally disconnected Hausdorff spa­ces", Dissertatias Math., 66 (1969).

R. L. Newcomb, "Topologices which are compact modulo an ideal", Ph. D. dissertation, Univ. of Cal. at Santa Barbara, 1967.

0. Njastad, "On some classes of nearly open sets", Pacific J. Math., 15 (1965), 961-970.

T. Noiri. "On S-closed spaces", Ann. Soc. Sci. Bruxelles, 91 (1977), 189-194.

----, "On RS-compact spaces", J. Korean Math. Soc., 22 {1985), No 1, pp. 19-34.

J. Porter and J. Thomas, "On H-closed and minimal Hausdorff spaces", Trans. Amer. Math. Soc., 138 (1969), pp. 159-170.

D. V. Rancin, "Compactness modulo an ideal", soviet Math. Dokl, Vol (13) (1972), No. 1, 193-197.

T. S. Thompson, "S-closed spaces", Proc. Amer. Math. Soc., 60 (1976), 335-338.

S. P. Young, "Local discrete extensions of topologies kyungpook", Math. J., 11 (1971), 21-24.

Downloads

Published

1993-12-01

How to Cite

EL-MONSEF, M. E. A., LASHIEN, E. F., & NASEF, A. A. (1993). S-COMPACTNESS VIA IDEALS. Tamkang Journal of Mathematics, 24(4), 431–443. https://doi.org/10.5556/j.tkjm.24.1993.4515

Issue

Section

Papers