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Between closed and Ig-closed sets

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2018

Key Words:

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Abstract (2. Language): 
The concept of closed sets is a central object in general topology. In order to extend many of important properties of closed sets to a larger families, Norman Levine initiated the study of generalized closed sets. In this paper we introduce, via ideals, new generalizations of closed subsets, which are strong forms of the Ig-closed sets, called Ig-closed sets and closed-I sets. We present some properties and applications of these new sets and compare the Ig-closed sets and the closed-I sets with the g-closed sets introduced by Levine. We show that I-closed and closed-I are independent concepts, as well as I-closed sets and closed-I concepts.
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REFERENCES

References: 

[1] V. Renuka Devi and D. Sivaraj. A generalization of normal spaces. Archivum Mathematicum,
44:265–270, 2008.
[2] S. Jafari and N. Rajesh. Generalized closed sets with respect to an ideal. Eur. Jour.
of Pure and App. Math, 4(2):147–151, 2011.
REFERENCES 314
[3] D. Jancovic and T. R. Hamlett. New topologies from old via ideals. Amer. Math.
Monthly, 97:295–310, 1990.
[4] D. Jancovic and T. R. Hamlett. Compatible extensions of ideals. Bollettino U. M.
I., (7):453–465, 1992.
[5] N. Levine. Generalized closed sets in Topology. Rend. Circ. Mat. Palermo, 19(2):89–
96, 1970.
[6] A. S. Mashhour, M. E. Abd El-Monsef, and S. N. El-Deep. On precontinuous and
weak precontinuous mappings. Proc. Math. and Phys. Soc. of Egypt, 53:47–53, 1982.
[7] Abd El Monsef, E. F. Lashien, and A. A. Nasef. On I-open sets and I-continuous
functions. Kyungpook Math. Jour., 32(1):21–30, 1992.
[8] R. L. Newcomb. Topologies which are compact modulo an ideal. PhD thesis, Univ. of
Calif. at Santa Barbara. California, 1967.
[9] N. R. Pachón. New forms of strong compactness in terms of ideals. Int. Jour. of Pure
and App. Math., 106(2):481–493, 2016.
[10] N. R. Pachón. C(I)-compact and I-QHC spaces. Int. Jour. of Pure and App.
Math., 108(2):199–214, 2016.
[11] J. Porter and J. Thomas. On H-closed and minimal Hausdorff spaces. Trans. Amer.
Math. Soc., 138:159–170, 1969.
[12] R. Vaidyanathaswamy. The localization theory in set-topology. Proc. Indian Acad.
Sci., 20:51–61, 1945.
[13] G. Viglino. C-compact spaces. Duke Mathematical Journal, 36(4):761–764, 1969.

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