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An Introduction to Inverse Limits with Set-valued Functions pp 13–46Cite as

Connectedness

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Abstract

A fundamental question about inverse limits with set-valued bonding functions relates to the connectedness of the inverse limit. For inverse limits on compact, connected factor spaces with bonding functions that are mappings, the inverse limit is always connected. However, for inverse limits with set-valued functions as bonding functions, the inverse limit is rarely connected. One might suspect that this is due to the fact that the graph of an upper semicontinuous function on a compact, connected space can fail to be connected, but the reasons go much deeper. In this chapter we study connectedness of inverse limits on [0,1] with set-valued functions.

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References

  1. Greenwood, S., Kennedy, J.: Connected generalized inverse limits. Topology Appl. 159, 57–68 (2012)

    MATH  MathSciNet  Google Scholar 

  2. Hurewicz, W.: Über oberhalb-stetige Zerlegungen von Punktmengen in Kontinua. Fund. Math. 15, 57–60 (1930)

    MATH  Google Scholar 

  3. Ingram, W.T.: Inverse limits with upper semi-continuous bonding functions: Problems and partial solutions. Topology Proc. 36, 353–373 (2010)

    MATH  MathSciNet  Google Scholar 

  4. Ingram, W.T.: Concerning nonconnected inverse limits with upper semi-continuous set-valued functions. Topology Proc. 40, 203–214 (2012)

    MathSciNet  Google Scholar 

  5. Ingram, W.T., Mahavier, W.S.: Inverse limits of upper semi-continuous set valued functions. Houston J. Math. 32, 119–130 (2006)

    MATH  MathSciNet  Google Scholar 

  6. Ingram, W.T., Mahavier, W.S.: Inverse limits: From continua to Chaos. In: Developments in Mathematics, vol. 25. Springer, New York (2012)

    Google Scholar 

  7. Mahavier, W.S.: Inverse limits with subsets of [0, 1] ×[0, 1]. Topology Appl. 141, 225–231 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  8. Moore, R.L.: Foundations of Point Set Theory, vol. 13, rev. edn. American Mathematical Society Colloquium Publications, Providence (1962)

    Google Scholar 

  9. Nadler, S.B., Jr.: Continuum Theory. Marcel-Dekker, New York (1992)

    MATH  Google Scholar 

  10. Nall, V.: Connected inverse limits with a set-valued function. Topology Proc. 40, 167–177 (2012)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Missouri University of Science and Technology, 1870 Miner Circle, Missouri, USA

    W. T. Ingram (Professor Emeritus)

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  1. W. T. Ingram
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© 2012 W.T. Ingram

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Ingram, W.T. (2012). Connectedness. In: An Introduction to Inverse Limits with Set-valued Functions. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4487-9_2

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