On Relative Preclosedness of Strongly Compact (Countably p-Compact) Sets

	International Journal of Mathematical Trends and Technology (IJMTT)
	© 2014 by IJMTT Journal
	Volume-6 Number-2
	Year of Publication : 2014
	Authors : Navpreet Singh Noorie , Anakh Singh
	10.14445/22315373/IJMTT-V6P519

Navpreet Singh Noorie , Anakh Singh. "On Relative Preclosedness of Strongly Compact (Countably p-Compact) Sets", International Journal of Mathematical Trends and Technology (IJMTT). V6:192-196 February 2014. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
In this paper, we study the preclosedness of strongly compact (countably p-compact) subsets of subspaces of strongly p-normal spaces. Consequences of the result for unions of specific sets are given. Examples are given to illustrate the results.

References

[1] M. Caldas, S. Jafari and T. Noiri, “Characterizations of pre-R0 and pre-R1 topological spaces”, Topology Proceedings, 25, 2000, 17-30.
[2] S. N. El-Deeb, I. A. Hasanein, A. S. Mashhour and T. Noiri, “On p-regular spaces”, Bull. Math. Soc. Sci. Math. R.S. Roumanie, 27, 1983, 311-315.
[3] M. Ganster, “Preopen sets and resolvable spaces”, Kyngpook, Math. J., 27(2), 1987, 135-143.
[4] G. L. Garg and N. Singh, “When a compact (countably compact) set is closed”, Acta. Math. Hungar., 94(3), 2002, 233-239.
[5] G. L. Garg and N. Singh, “When a compact (countably compact) set is closed II”, Acta. Math. Hungar., 105(4), 2004, 331-337.
[6] S. Jafari and T. Noiri, “More on strongly compact spaces”, Missouri J. Math. Sci., 19(1), 2007, 52-61.
[7] A. Kar and P. Bhattacharyya, “Some weak separation axioms”, Bull Calcutta Math.Soc., 82, 1990, 415-422.
[8] 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.
[9] A. S. Mashhour, M. E. Abd El-Monsef, I. A. Hasanein and T. Noiri, “Strongly compact spaces”, Delta J. Sci., 8 (1), 1984, 30–46.
[10] N. S. Noorie and A. Singh, “Charachterizations of pre-R0, pre-R1 spaces and p*closedness of strongly compact (countably p-compact) sets”, Journal of Advanced Studies in Topology, 5(1), 2014, 50-56.
[11] Paul and Bhattacharyya, “On p-normal spaces”, Soochow J. Math., 21(3), 1995, 273-289.
[12] Paul and Bhattacharyya, “On Pre-Urysohn Space”, Bull, Malaysian Math. Soc. (Second Series), 22, 1999, 23-34.
[13] L. A. Steen and J. A. Seebach, Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., 1970.
[14] S. S. Thakur and P. Paik, “Countably p-compact spaces”, Sci. Phys. Sci., 1(1), 1989, 48–51.
[15] A. Wilansky, Topology for Analysis, Xerox College Publishing, Lexington, Massa-chusetts, Toronto, 1970.

Keywords
preclosed, p*closed, pre-R1, strongly compact, countably p-compact, pre-accumulation, p-convergent, pre-sequential, strongly p-normal, net.