EXTENSIONS GENERATED BY CLOSED SETS

Authors

  • M. E ABD EL-MONSEF Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.
  • A. M. KOZAE Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.
  • A. A. ABO-KHADRA Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.

DOI:

https://doi.org/10.5556/j.tkjm.25.1994.4488

Keywords:

extension of spaces, compactification, cid spaces, normal space

Abstract

From the nonempty collection of all closed sets $(Y)$ of any topological space $(X , \tau)$, Schmidt generates a topological space $(Y,\mathcal{U})$. In this paper, we give some properties of this topological space. We determined when $(f,(Y,\mathcal{U}))$ is an extension of $(X , \tau)$. Also we give some separation properties. This paper leads us to unsolved problem men- tioned at the encl of it.

References

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I. L. Reilly, M. K. Vamanamurthy, "On spaces in which every denumerable subspace is discrete," Math. Vesnik 38 (1986), 97-102.

IL J. Schmidt, "llyperspaccs of quotient and subspaces," I. Hausdorff topological spaces. Math. Naeher 104 (1981), 271-280.

H. J. Schmidt, "Hyperspaces of quotient and subspaces," II. Metrizable spaces. Math. Nachr. 104 (1981), 281-288.

L. A. Steen and J. A. Seebach, "Counterexamples in topology," Springer-Verlag, New York 1978.

W . J. Thron, "Topological structrs," Holt, Rinehart and Winston, Inc, New York (1966).

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Published

1993-06-01

How to Cite

EL-MONSEF, M. E. A., KOZAE, A. M., & ABO-KHADRA, A. A. (1993). EXTENSIONS GENERATED BY CLOSED SETS. Tamkang Journal of Mathematics, 24(2), 189-193. https://doi.org/10.5556/j.tkjm.25.1994.4488

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