A NOTE ON EXTENSIONS GENERATED BY CLOSED SETS

Article Sidebar

PDF
Published: Jun 1, 1995
DOI: https://doi.org/10.5556/j.tkjm.26.1995.4386
Keywords:
Extension of spaces hyperspace

Main Article Content

Maximilian Ganster
Department of Mathematics, Graz Univesity of Technology, Steyrerga.sse 30, A-8010 Graz; AUSTRIA.

Abstract




In a recent paper Abd El-Monsef et al. consider a certain topology on $2^X$ where $2^X$ is the family of all nonempty closed subsets of a given topological space $X$. Vnfortunately, several results in their paper are incorrect and so the purpose of this note is to correct, improve and expand these results. In addition, the main quesion in their paper turns out to have a quite simple answer.




Article Details

How to Cite
Ganster, M. (1995). A NOTE ON EXTENSIONS GENERATED BY CLOSED SETS. Tamkang Journal of Mathematics, 26(2), 125–129. https://doi.org/10.5556/j.tkjm.26.1995.4386
Issue
Vol. 26 No. 2 (1995)
Section
Papers
Creative Commons License

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

References

M. E. Abd El-Monsef, A. M. Kozae and A. A. Abo-Khadra, "Extensions generated by closed sets," Tamkang J. Math., 24 (1993), 189-193

N. Bourbaki, General Topology, Part 1, Addison-Wesley, Reading, Mass. 1966.

E. Michael, "Topologies on spaces of subsets," Trans. Amer. Math. Soc., 71 (1951), 152-182

H. J. Schmidt, "Hyperspaces of quotient and subspaces I." Hausdorff topological spaces, Math Nachr., 104 (1981), 271-280.