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Categorical and Cardinal Properties of Hyperspaces with a Finite Number of Components

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Abstract

In this paper, we examine categorical and cardinal properties of hyperspaces with finite number of components. We prove that the functor Cn : Comp → Comp is not normal, i.e., it does not preserve epimorphisms of continuous mappings. We also discuss the density, the caliber, and the Shanin number of the space Cn(X).

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References

  1. P. S. Alexandroff and P. S. Urysohn, Memoire sur les espaces topologiques compacts, Verh. Akad. Wetensch. Amsterdam (1929), No. 14.

    MATH  Google Scholar 

  2. R. B. Beshimov, “Weak density and hyperspaces,” Uzbek. Mat. Zh., 4, 3–7 (2000).

    Google Scholar 

  3. R. B. Beshimov, “A note on weakly separable spaces,” Math. Moravica, 6, 9–19 (2002).

    Article  MathSciNet  Google Scholar 

  4. R. B. Beshimov, “Some cardinal properties of topological spaces connected with weakly density,” Methods Funct. Anal. Topol., 10, No. 3, 17–22 (2004).

    MathSciNet  MATH  Google Scholar 

  5. J. Camargo and S. Macias, “Quotients of n-fold hyperspaces,” Topol. Appl., 197, 154–166 (2016).

    Article  MathSciNet  Google Scholar 

  6. R. Engelking, General Topology, Heldermann, Berlin (1989).

    MATH  Google Scholar 

  7. V. V. Fedorchuk and V. V. Filippov, General Topology. Fundamental Constructions [in Russian], Moscow (2014).

  8. Y. Hattory, “Order and topological structures of posets of the formal balls on metric spaces,” Mem. Fac. Sci. Eng. Shimane Univ. Ser. B. Math. Sci., No. 43, 13–26 (2010).

  9. S. Macias, “On n-fold hyperspaces of continua,” Glas. Mat., 64, No. 44, 479–492 (2009).

    Article  MathSciNet  Google Scholar 

  10. E. V. Shchepin, “Functors and uncountable powers of compacta,” Usp. Mat. Nauk, 36, No. 3 (219), 3–62 (1981).

    Article  Google Scholar 

  11. R. H. Sorgenfrey, “On the topological product of paracompact spaces,” Bull. Am. Math. Soc., 53, 631–632 (1947).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan

    R. B. Beshimov & Sh. Kh. Eshtemirova

  2. Uzbekistan Academy of Sciences, V. I. Romanovskiy Institute of Mathematics, Tashkent, Uzbekistan

    N. K. Mamadaliev

Authors
  1. R. B. Beshimov
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  2. N. K. Mamadaliev
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  3. Sh. Kh. Eshtemirova
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Corresponding author

Correspondence to R. B. Beshimov.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 144, Proceedings of the Conference “Problems of Modern Topology and Its Applications” (May 11–12, 2017), Tashkent, Uzbekistan, 2018.

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Beshimov, R.B., Mamadaliev, N.K. & Eshtemirova, S.K. Categorical and Cardinal Properties of Hyperspaces with a Finite Number of Components. J Math Sci 245, 390–397 (2020). https://doi.org/10.1007/s10958-020-04701-8

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  • DOI: https://doi.org/10.1007/s10958-020-04701-8

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