ON REGULAR SEMI-OPEN SETS AND $S^*$-CLOSED SPACES

Authors

  • S. F. TADROS Department of Mathematics, Faculty of Science, University of Mansoura, Mansoura, EGYPT .
  • A. B. KHALAF Department of Mathematics, Faculty of Science, University of Mansoura, Mansoura, EGYPT.

DOI:

https://doi.org/10.5556/j.tkjm.23.1992.4557

Keywords:

regular semi-open sets, S-closed spaces, nearly compact spaces, regular semi-open cover

Abstract

In this note, the regular semi-open sets, introduced in [2], are further investigated. Using covers consisting of such sets, a new class of topological spaces, called the $s^*$-closed spaces, is defined and studied.

References

M. E. Abd El- Monsef, S. N. El- Deeb and R. A. Mahmoud, "beta- open sets and beta一cont­inuous mappings", Bull. Fae. Sci. Assiut Univ. (1983) 1-18.

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

S. G. Crossley and S. K. Hildebrancl, "Semi- closure, Taxas", J. Sci. 22 (2+ 3) (1971), 99- 112.

R. A. Herrman, "RC- convergence", Proc. Amer. Math. Soc., 75 (1979), 311-317.

T. Husain, "Topology and maps", Plenum Press, 1977.

N. Levine, "Semi-open sets and semi-continuity in topological spaces", Amer. Math. Monthly, 10 (1963) 36-41 MR 29 # 4025

S. N. Maheshwari and R. Prasad, "On s-regular spaces", Glasnik Mat. Ser. III 10(30) (1975), 347-350.

A. S. Mashour, M. E. Abd El-Monsef , S. N. El-Deeb, "On pre-continuous and week pre-continuous mappings", Proc. Math. Phys. Soc. Egypt 53 (1982), 47-53.

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

T. Noiri, "On semi-continuous mappings", Alfi. Accad. Naz. Lincei Rend. Cl. Sci. Fiz. Mat. Natur 8 (54) (1973), 210-214.

T. Noiri, "Properties of s-closed spaces", Acta Math. Acad. Sci. Hung. 53 (3-4) (1980), 431-436.

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

M. K. Singal S. P. Arya, "On almost regular spaces", Glasnik Mat. Ser. III (4) 24 (1969), 89-99.

M. K. Singal and A. Mathur, "On nearly compact spaces", Boll. Un. Math. Ital., (4) 2 (1969), 702-710.

S. F. Tadros and A. S. Abd Allah, "On some mappings of topological spaces", Accepted in Ain Shams Univ. Sci. Bull.

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

Downloads

Published

1992-12-01

How to Cite

TADROS, S. F., & KHALAF, A. B. (1992). ON REGULAR SEMI-OPEN SETS AND $S^*$-CLOSED SPACES. Tamkang Journal of Mathematics, 23(4), 337–348. https://doi.org/10.5556/j.tkjm.23.1992.4557

Issue

Section

Papers