Ig #-Normal and I g#-Regular Spaces
Keywords:
I g# -closed and Ig# -open set, completely codense ideal, g#-closed and g#-open set, g#-normal space, mildly normal space, regular space
Abstract
I g# -normal and Ig# -regular spaces are introduced and various characterizations and properties are given. Characterizations of normal, mildly normal, g#-normal and regular spaces are also given.
References
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J.Dontchev, M.Ganster and D.Rose, Ideal resolvability, Topology and its Applications, 93(1999), 1-16.
E.Hayashi, Topologies defined by local properties, Math. Ann., 156(1964), 205-215.
D.Jankovic and T.R.Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97(4)(1990), 295-310.
M.Kamaraj, V.Ba.Vijeyrani and O.Ravi, g#-closed sets in ideal topological spaces, International Journal of Mathematics And its Applications, 4(2-C)(2016), 73-83.
K.Kuratowski, Topology, Vol. I, Academic Press, New York, (1966).
N.Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19(2)(1970), 89-96.
H.Maki, R.Devi and K.Balachandran, Associated topologies of generalized α-closed sets and α-generalized closed sets, Mem. Fac. Sci. Kochi Univ. Math., 15(1994), 51-63.
A.S.Mashhour, M.E.Abd El-Monsef and S.N.El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phy. Soc. Egypt, 53(1982), 47-53.
A.S.Mashhour, I.A.Hasanein and S.N.El-Deeb, α-continuous and α-open mappings, Acta Math. Hungar., 41(1983), 213-218.
M.Navaneethakrishnan, Ph.D Thesis, Manonmaniam Sundaranar University, Tirunelveli, Tamil Nadu, India, (2009).
O.Njastad, On some classes of nearly open sets, Pacific J. Math., 15(3)(1965), 961-970.
T.Noiri, Almost αg-closed functions and separation axioms, Acta Math. Hungar., 82(3)(1999), 193-205.
N.Palaniappan and K.C.Rao, Regular generalized closed sets, Kyungpook Math. J., 33(2)(1993), 211-219.
V.Renuka Devi, D.Sivaraj and T.Tamizh Chelvam, Codense and completely codense ideals, Acta Math. Hungar., 108(3)(2005), 197-205.
M.K.Singal and A.R.Singal, Mildly normal spaces, Kyungpook Math. J., 13(1973), 27-31.
M.H.Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 375-481.
R.Vaidyanathaswamy, Set Topology, Chelsea Publishing Company, (1946).
M.K.R.S.Veerakumar, g#-closed sets in topological spaces, Mem. Fac. Sci. Kochi Univ. Math., 24(2003), 1-13.
J.Dontchev, M.Ganster and D.Rose, Ideal resolvability, Topology and its Applications, 93(1999), 1-16.
E.Hayashi, Topologies defined by local properties, Math. Ann., 156(1964), 205-215.
D.Jankovic and T.R.Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97(4)(1990), 295-310.
M.Kamaraj, V.Ba.Vijeyrani and O.Ravi, g#-closed sets in ideal topological spaces, International Journal of Mathematics And its Applications, 4(2-C)(2016), 73-83.
K.Kuratowski, Topology, Vol. I, Academic Press, New York, (1966).
N.Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19(2)(1970), 89-96.
H.Maki, R.Devi and K.Balachandran, Associated topologies of generalized α-closed sets and α-generalized closed sets, Mem. Fac. Sci. Kochi Univ. Math., 15(1994), 51-63.
A.S.Mashhour, M.E.Abd El-Monsef and S.N.El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phy. Soc. Egypt, 53(1982), 47-53.
A.S.Mashhour, I.A.Hasanein and S.N.El-Deeb, α-continuous and α-open mappings, Acta Math. Hungar., 41(1983), 213-218.
M.Navaneethakrishnan, Ph.D Thesis, Manonmaniam Sundaranar University, Tirunelveli, Tamil Nadu, India, (2009).
O.Njastad, On some classes of nearly open sets, Pacific J. Math., 15(3)(1965), 961-970.
T.Noiri, Almost αg-closed functions and separation axioms, Acta Math. Hungar., 82(3)(1999), 193-205.
N.Palaniappan and K.C.Rao, Regular generalized closed sets, Kyungpook Math. J., 33(2)(1993), 211-219.
V.Renuka Devi, D.Sivaraj and T.Tamizh Chelvam, Codense and completely codense ideals, Acta Math. Hungar., 108(3)(2005), 197-205.
M.K.Singal and A.R.Singal, Mildly normal spaces, Kyungpook Math. J., 13(1973), 27-31.
M.H.Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 375-481.
R.Vaidyanathaswamy, Set Topology, Chelsea Publishing Company, (1946).
M.K.R.S.Veerakumar, g#-closed sets in topological spaces, Mem. Fac. Sci. Kochi Univ. Math., 24(2003), 1-13.
How to Cite
K.Meena, O.Nethaji, & O.Ravi. (2016). Ig #-Normal and I g#-Regular Spaces. International Journal of Current Research in Science and Technology, 2(11), 1-10. Retrieved from https://crst.gfer.org/index.php/crst/article/view/74
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