Abstract
The purpose of this paper is to introduce ideal minimal spaces and to investigate the relationships between minimal spaces and ideal minimal spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.
Similar content being viewed by others
References
M. Alimohammady and M. Roohi, Fixed point in minimal spaces, Nonlinear Anal. Model. Control, 10 (2005), 305-314.
M. Alimohammady and M. Roohi, Linear minimal space, Chaos Solitons Fractals, 33 (2007), 1348–1354.
Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (2002), 351–357.
J. Dontchev, M. Ganster and T. Noiri,Unified operation apporoach of generalized closed sets via topological ideals, Math. Japonica, 49 (1999), 395–401.
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.
D. Janković and T. R. Hamlett, Compatible extensions of ideals, Boll. Un. Mat. Ital., B(7)6, (1992), 453–465.
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, J. Umehara and T. Noiri, Every topological space is preT1/2, Mem. Fac. Sci. Kochi Univ. Ser. A Math., 17 (1996), 33–42.
H. Maki, On generalizing semi-open sets and preopen sets, in: Meeting on Topological Spaces Theory and its Application (August, 1996), pp. 13–18.
M. Murugalingam, A Study of Semi Generalized Topology, Ph. D. Thesis, Manonmaniam Sundaranar Univ. (Tirunelveli, Tamil Nadu, India, 2005).
M. Navaneethakrishnan and J. Paulraj Joseph, g-closed sets in ideal topological spaces, Acta Math. Hungar., 119 (2008), 365–371.
T. Noiri and V. Popa, On m-D-separation axioms, J. Math. Univ. Istanbul Fac. Sci., 61/62 (2002/2003), 15–28.
T. Noiri and V. Popa, Between closed sets and g-closed sets, Rend. Circ. Mat. Palermo (2), 55 (2006), 175–184.
V. Popa and T. Noiri, On m-continuous functions, Anal. Univ. “Dunârea de Jos” Galati, Ser. Mat. Fiz. Mec. Teor. (2), 18 (2000), 31–41.
R. Vaidyanathaswamy, The localization theory in set topology, Proc. Indian Acad. Sci., Sect A, 20 (1944), 51–61.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ozbakir, O.B., Yildirim, E.D. On some closed sets in ideal minimal spaces. Acta Math Hung 125, 227–235 (2009). https://doi.org/10.1007/s10474-009-8240-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-009-8240-9