Skip to main content
SpringerLink
Log in

The (Weak) Full Projection Property for Inverse Limits with Upper Semicontinuous Bonding Functions

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

We give new results about the full projection property and the weak full projection property for inverse limits with upper semicontinuous bonding functions. This solves several problems stated by W. T. Ingram.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arkhangel’skii, A.V., Ponomarev, V.I.: Fundamentals of General Topology: Problems and Exercises. D. Reidel Publishing Co., Dordrecht (1984)

    Google Scholar 

  2. Banič, I., Kennedy, J.: Inverse limits with bonding functions whose graphs are arcs. Topol. Appl. 196, 155–172 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  3. Banič, I., Črepnjak, M., Merhar, M., Milutinović, U.: Inverse limits, inverse limit hulls and crossovers. Topol. Appl. 196, 155–172 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Banič, I., Črepnjak, M., Merhar, M., Milutinović, U., Sovič, T.: The closed subset theorem for inverse limits with upper semicontinuous bonding functions. Bull. Malays. Math. Sci. Soc. (2017). https://doi.org/10.1007/s40840-017-0517-5

    MATH  Google Scholar 

  5. Davies, G., Greenwood, S., Lockyer M., Maehara, Y.: Inverse Limits of Upper Semicontinuous Functions and Indecomposable Continua (2016) (preprint)

  6. Gruenhage, G.: Irreducible restrictions of closed mappings. Topol. Appl. 85, 127–135 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ingram, W.T.: An Introduction to Inverse Limits with Set-Valued Functions. Springer, New York (2012)

    Book  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  9. Kelly, J.P.: Inverse limits with irreducible set-valued functions. Topol. Appl. 166, 15–31 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kelly, J.P., Meddaugh, J.: Indecomposability in inverse limits with set-valued functions. Topol. Appl. 160, 1720–1731 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lončar, I.: Hereditarily irreducible mappings of Cartesian product of continua. Sarajevo J. Math. 7, 115–121 (2011)

    MathSciNet  MATH  Google Scholar 

  12. Mahavier, W.S.: Inverse limits with subsets of \( [0,1]\times [0,1]\). Topol. Appl. 141, 225–231 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Nadler, S.B.: Continuum theory. In: An Introduction, Monographs and Textbooks in Pure and Applied Mathematics, vol. 158. Marcel Dekker, Inc., New York (1992)

  14. Porter, J.R., Woods, R.G.: Extensions and Absolutes of Hausdorff Spaces. Springer, New York (1987)

    MATH  Google Scholar 

  15. Varagona, S.: Inverse limits with upper semi-continuous bonding functions and indecomposability. Houst. J. Math. 37, 1017–1034 (2011)

    MathSciNet  MATH  Google Scholar 

  16. Varagona, S.: Homeomorphisms between inverse limits with N-shaped set-valued functions. Topol. Proc. 44, 233–248 (2014)

    MathSciNet  MATH  Google Scholar 

  17. Williams, B.R.: Indecomposability in Inverse Limits. Ph.D. Dissertation, Baylor University (2010)

Download references

Acknowledgements

The authors wish to thank the anonymous referee for his comments.

Author information

Authors and Affiliations

  1. Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, 2000, Maribor, Slovenia

    Iztok Banič, Matevž Črepnjak, Matej Merhar & Uroš Milutinović

  2. Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000, Ljubljana, Slovenia

    Iztok Banič & Uroš Milutinović

  3. Andrej Marušič Institute, University of Primorska, Muzejski trg 2, 6000, Koper, Slovenia

    Iztok Banič & Matevž Črepnjak

  4. Faculty of Chemistry and Chemical Engineering, University of Maribor, Smetanova 17, 2000, Maribor, Slovenia

    Matevž Črepnjak

Authors
  1. Iztok Banič
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matevž Črepnjak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Matej Merhar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Uroš Milutinović
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Iztok Banič.

Additional information

This work is supported in part by the Slovenian Research Agency (research programs P1-0285 and P1-0297, and research projects J1-5433 and J1-7110).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Banič, I., Črepnjak, M., Merhar, M. et al. The (Weak) Full Projection Property for Inverse Limits with Upper Semicontinuous Bonding Functions. Mediterr. J. Math. 15, 167 (2018). https://doi.org/10.1007/s00009-018-1209-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00009-018-1209-6

Keywords

Mathematics Subject Classification

Search

Navigation