A NOTE ON SPACES VIA DENSE SETS

Article Sidebar

PDF
Published: Sep 1, 1993
DOI: https://doi.org/10.5556/j.tkjm.24.1993.4505
Keywords:
Resolvable space, irresolvable space, hereditarily irresolvable space, submaximal space, preopen set, semi-open set, SMPC, precontinuity, preirresolute, semi-open function, Hewitt representation

Main Article Content

R. A. MAHMOUND
Department of Mathematics, Faculty of Science, Menoufia University, Egypt.
D. A. ROSE
Dcpartment of Mathematics, East Central University, Oda, Oklahoma, 74820, U. S. A.

Abstract




Some spaces have been defined depending on the concept of dense set in a given topological space $(X , \tau)$ such as: resolvable space, irresolvable space, hcreditarily irresolvable space, and submaximal space. We study many of their properties and explore several relationships between these spaces and SMPC function which has been defined recently as a dual of the concept of precontmuity.




Article Details

How to Cite
MAHMOUND, R. A., & ROSE, D. A. (1993). A NOTE ON SPACES VIA DENSE SETS. Tamkang Journal of Mathematics, 24(3), 333–339. https://doi.org/10.5556/j.tkjm.24.1993.4505
Issue
Vol. 24 No. 3 (1993)
Section
Papers
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

References

M. Ganster, "Preopen sets and resolvable spaces", to appear in Kyungpook Math. J.

E. Hewitt, "A problem of set theoretic topology", Duke Math. J. 10 (1943), 309-333.

D. E. Cameron, "A Class of maximal topologies", Pacific J. of Math., 7 (1977), 101-104.

A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, "On precontinuous and weak- precontinuous mappings", Proc. Math. and Phys. Soc. Egypt, 53 (1982), 47-53.

A. S. Ma.shhour, I. A. Ha.sanem and S. N. El-Deeb, "a-continuous and a-open mappings", Acta Math. Acad. Sci. Hungar, 41 (1983), 213-218.

N. Levine, "Semi-open sets and semi-continuity in topological spaces", Amer. Math. Monthly, 70 (1963), 36-41.

A. D. Rose, "Subweakly a-continuous functions", Inter. J. of Math. and Math. Sci., 11 (1988), 713-720.

I. L. Reilly and M. K. Vamanamurthy, "On a-continuity in topological spaces", Acta Math. Hungar, 45 (1985), 27-32.

R. A. Mahmoud, M. E. Abd El-Monsef and A. A. Na.sef, "A Class of functions stroger than M -precontinuous, preirresolute and A-function", to appear in Qatar Univ. Sci.. Bull.

D. S. Jankovic, "A Not on mapping of extremally disconnected spaces", Acta. Math. Hungar, 46 (1985), 83-92.

S. G. Grossely, and S. K. Hildebrand, "Semi-topological properties", Fund. Math., 74 (1972), 233-254.