ON SUBMAXIMAL SPACES
Main Article Content
Abstract
A topological space $X$ is called submaximal if every dense subset of $X$ is open. In this paper, which is an enlarged version of Section 3 in [7], we characterize submaximal spaces using various topological notions. We study the connections between submaximal and related spaces as well as we improve some results concerning submaximal space achieved by Mahmoud and Rose in [7].
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
References
N. Bourbaki, General Topology, Addison-Wesley, Mass., 1966.
N. Bourbaki, Elements de mathematique, Algebre commutative, Chap. 2., Hermann, Paris, 1961.
D. Jankovic, I. Reilly and M. Vamanamurthy, "On strongly compact topological spaces," Q & A in General Topology, 6 (1) (1988), 29-40.
N. Levine, "Generalized closed sets in topolgy," Rend. Circ. Mat. Palermo, 19 (2) (1970), 89-96.
N. Levine, "Semi-open sets and semi-continuity in topological spaces," Amer. Math. Monthly, 70 (1963), 36-41.
N. Levine, "The superset topology," Amer. Math. Monthly, 75 (1968), 745-746.
R. A. Mahmoud and D. A. Rose, "A note on spaces via dense sets," Tamkang J. Math., 24 (3)(1993), 333-339.
A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, "On pre-continuous and weak pre-continuous mappings," Proc. Math. Phys. Soc. Egypt, 53 (1982), 47-53.
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.
T. Nieminen, Lectures in general topology, unpublished, (in Finnish).
0 . Njastad, "On some classes of nearly open sets," Pacific J. Math., 15 (1965), 961-970.
P. L. Sharma, "A class of spaces in which compact sets are finite," Canadian Math. Bull., 24 (1981), 373-375.
J. Tong, "On decomposition of continuity in topological spaces," Acta Math. Hung., 54 (1989), 51- 55.
S. Willard, General Topology, Addison-Wesley, 1970.