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Making Holes in the Hyperspace of Subcontinua of Some Continua

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DOI: 10.4236/apm.2012.22020    4,344 Downloads   7,792 Views   Citations

ABSTRACT

Let be a metric continuum. Let , is said to make a hole in , if is not unico-herent. In this paper, we characterize elements such that makes a hole in , where is either a smooth fan or an Elsa continuum.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

J. Anaya, E. Castañeda-Alvarado and F. Orozco-Zitli, "Making Holes in the Hyperspace of Subcontinua of Some Continua," Advances in Pure Mathematics, Vol. 2 No. 2, 2012, pp. 133-138. doi: 10.4236/apm.2012.22020.

References

[1] A. Illanes and S. B. Nadler Jr., “Hyperspaces: Fundamentals and Recent Advances,” Marcel Dekker, Inc., New York, 1999.
[2] J. G. Anaya, “Making Holes in Hyperspaces,” Topology and Its Applications, Vol. 154, No. 10, 2007, pp. 2000- 2008. doi:10.1016/j.topol.2006.09.017
[3] J. G. Anaya, “Making Holes in the Hyperspace of Subcontinua of a Peano Continuum,” Topology Proceedings, Vol. 37, 2011, pp. 1-14.
[4] S. Eilenberg, “Transformations Continues en Circonférence et la Topologie du Plan,” Fundamenta Mathematicae, Vol. 26 1936, pp. 61-112.
[5] C. Eberhart, “A Note on Smooth Fans,” Colloquium Mathematicum, Vol. 20, 1969, pp. 89-90.
[6] C. Eberhart and S. B. Nadler Jr., “Hyperspaces of Cones and Fans,” Proceedings of the American Mathematical Society, Vol. 77, No. 22, 1979, pp. 279-288. doi:10.1090/S0002-9939-1979-0542098-5
[7] S. B. Nadler Jr., “Continua Whose Cone and Hyperspace Are Homeomorphic,” Transactions of the American Mathematical Society, Vol. 230, 1977, pp. 321-345. doi:10.1090/S0002-9947-1977-0464191-0
[8] S. B. Nadler Jr., “Arc Components of Certain Chainable Continua,” Canadian Mathematical Bulletin, Vol. 14, No. 2, 1971, pp. 183-189. doi:10.4153/CMB-1971-033-8
[9] S. B. Nadler Jr., “Continuum Theory: An Introduction,” Marcel Dekker, Inc., New York, 1992.
[10] A. Illanes, “Multicoherence of Whitney levels,” Topology and Its Applications, Vol. 68, No. 3, 1996, pp. 251-265. doi:10.1016/0166-8641(95)00064-X
[11] W. J. Charatonik, “Some Counterexamples Concerning Whitney Levels,” Bull. Polish. Acad. Sci. Math., Vol. 31, 1983, pp. 385-391.
[12] C. B. Hughes, “Some properties of Whitney continua in the hyperspace C(X),” Topology Proceedings, Vol. 1, 1976, pp. 209-219.

  
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