New types of generalizations of θ-closed sets

  • Y. Gh. Gouda Mathematics department, Aswan University, faculty of science, Aswan, Egypt
  • M. M. El-Sharkasy Mathematics department, Tanta University, faculty of science, Mathematics department, Tanta, Egypt
  • S. M. El-Sayed Mathematics department, Faculty of science, Aswan university, Egypt
Keywords: T-closed sets, generalized T-closed sets, θ -closed sets

Abstract

The aim of this paper is to introduce and study the class of T-closed sets as a generalization of θ-closed sets, which is properly placed between θ-closed sets and closed sets. A generalization of T-closed sets, namely, generalized T-closed sets is introduced and studied, which is properly placed between T-closed sets and g-closed sets.

Downloads

Download data is not yet available.

References

N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl. 78(1968), 103-118. Zbl 183.27302.

J. Dontchev and H. Maki, On θ-generalized closed sets, Internat. J. Math. & Math. Sci. 22 (1999), 239-249.

N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo 19(2) (1970), 89-96.

W. Dunham, A new closure operator for non-T1 topologies, Kyungpook Math. J., 22(1982), 55-60.

S. Lipschutz , Theory and problems of general topology, Schums series (1986).

N. Levine, An equivalence relation in topology, Mathematical journal of Okayama University, Vol. 15(1971), Iss. 2, Art. 3, 113-123.

P. Bhattacharyya and B. K. Lahiri, Semigeneralized closed sets in topology, Indian J. Math. 29(1987), no. 3, 375-382.

H. Maki, R. Devi, and K. Balachandran, Generalized -closed sets in topology, Bull. Fukuoka Univ. Ed. III 42(1993), 13-21.

S. P. Arya and T. M. Nour, Characterizations of s-normal spaces, Indian J. Pure Appl. Math. 21(1990), no. 8, 717-719.

H. Maki, R. Devi and K. Balachandran,Associated topologies of generalized -closed sets and-generalized closed sets, Mem. Fac. Sci. Kochi Univ. Ser. A Math.15(1994), 51-63.

J. Dontchev, On generalizing semi-preopen sets, Mem. Fac. Sci. Kochi Univ. Ser. A Math. 16(1995), 35-48.

N. Palaniappan and K. C. Rao, Regular generalized closed sets, Kyungpook Math. J. 33 (1993), no. 2, 211-219.

O. Najsted. "on some classes of nearly open sets" Pacific. J. Math. 15 (1965) 961-970.

N. Levine. ”Semi open sets and semi continuous mappings in topological spaces” Amr.Math. Monthly 70 (1963) 36-41.

D. Andrijevi´c, Semipreopen sets, Mat. Vesnik 38 (1986), no. 1, 24–32.

A. S. Mashhour, I. A. Hasanein, S. N. El-Deeb, α-continuous and α-open mappings, Acta Math.Phys. Soc. Egypt, 51 (1981).

S. G. Crossley, S. K. Hildebrand, Semi-closure, Texas J. Sci. 22 (1971), 99-112.

M. Caldas, S. Jafari, M. M. Kovar, Some Properties of θ-open Sets, Divulgaciones Matematicas Vol. 12 No. 2(2004), pp. 161-169

T. Noiri, S. Jafari, Properties of (θ, s)-continuous functions, Topology and its Applications, 123(1)(2002), 167-179.

J. Cao, M. Ganster and I. Reilly, On generalized closed sets, Topology & Appl. 123 (2002), 37-46.

Mohamed Saleh, On θ-closedsetsandsome forms of continuity, archivummathematicum (BRNO), Tomus 40 (2004), 383 – 393.

W. Dunham, T_(1/2)-spaces, Kyungpook Math. J., V. 17, No. 2, December 1977.

M.H. Stone, Applications of the theory of Boolean rings to general

topology, Trans. Amer. Math. Soc., 41 (1937), 375-381.

Published
2016-07-07
How to Cite
Gouda, Y. G., El-Sharkasy, M. M., & El-Sayed, S. M. (2016). New types of generalizations of θ-closed sets. Journal of Progressive Research in Mathematics, 8(2), 1249-1257. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/801
Section
Articles