Abstract
\( \mathcal{I}_g \)-normal and \( \mathcal{I}_g \)-regular spaces are introduced and various characterizations and properties are given. Characterizations of normal, mildly normal, g-normal, regular and almost regular spaces are also given.
Similar content being viewed by others
References
J. Dontchev, M. Ganster and T. Noiri, Unified approach of generalized closed sets via topological ideals, Math. Japonica, 49 (1999), 395‘401.
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. Janković and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97 (1990), 295‘310.
K. Kuratowski, Topology, Vol. I, Academic Press (New York, 1966).
N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo (2), 19 (1970), 89‘96.
H. Maki, R. Devi and K. Balachandran, Associated topologies of generalized ?-closed sets and ?-generalized closed sets, Mem. Fac. Sci. Kochi Univ. Math., 15 (1994), 51‘63.
H. Maki, R. Devi and K. Balachandran, Generalized ?-closed sets in topology, Bull. Fukuoka Univ. Ed, III., 42 (1993), 13‘21.
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.
B. M. Munshi, Separation Axioms, Acta Ciencia Indica, 12 (1986), 140‘144.
M. Navaneethakrishnan and J. Paulraj Joseph, g-closed sets in ideal topological spaces, Acta Math. Hungar., 119 (2008), 365‘371.
O. Njästad, On some classes of nearly open sets, Pacific J. Math., 15 (1965), 961‘970.
T. Noiri, Almost ?g-closed functions and separation axioms, Acta Math. Hungar., 82 (1999), 193‘205.
T. Noiri and V. Popa, On g-regular spaces and some functions, Mem. Fac. Sci. Kochi Univ. Math., 20 (1999), 67‘74.
V. Renuka Devi, D. Sivaraj and T. Tamizh Chelvam, Codense and completely codense ideals, Acta Math. Hungar., 108 (2005), 197‘205.
M. K. Singal and S. P. Arya, On almost-regular spaces, Glasnik Mat., 4 (1969), 89‘99.
M. K. Singal and A. R. Singal, Mildly normal spaces, Kyungpook Math. J., 13 (1973), 27‘31.
R. Vaidyanathaswamy, Set Topology, Chelsea Publishing Company (1946).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Navaneethakrishnan, M., Paulraj Joseph, J. & Sivaraj, D. \( \mathcal{I}_g \)-normal and \( \mathcal{I}_g \)-regular spaces. Acta Math Hung 125, 327–340 (2009). https://doi.org/10.1007/s10474-009-9027-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-009-9027-8
Key words and phrases
- \( \mathcal{I}_g \)-closed
- \( \mathcal{I}_g \)-open set
- completely codense ideal
- g-closed and g-open set
- g-normal space
- mildly normal and almost regular space