Skip to main content
SpringerLink
Log in

Hyperspaces of dimension 1

  • Original Article
  • Published:
Boletín de la Sociedad Matemática Mexicana Aims and scope Submit manuscript

Abstract

In a previuos paper the author asked if there exists a one-dimensional space X that is not almost zero-dimensional, such that the dimension of the hyperspace of compact subsets of X is one-dimensional. In this short note we give examples of spaces X that are not almost zero-dimensional such that X is one-dimensional and their hyperspace of compacta of X also is one-dimensional.

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. Dijkstra, J.J., van Mill, J.: Erdős space and homeomorphism groups of manifolds. Mem. Amer. Math. Soc 208, 979 (2010)

    MATH  Google Scholar 

  2. Erdős, P.: The dimension of the rational points in Hilbert space. Ann. Math. 41, 734–736 (1940)

    Article  MathSciNet  Google Scholar 

  3. Kawamura, K., Oversteegen, L., Tymchatyn, E.D.: On homogeneous totally disconnected 1-dimensional spaces. Fund. Math. 150(2), 97–112 (1996)

    Article  MathSciNet  Google Scholar 

  4. Abry, M., Dijkstra, J.J., Van Mill, J.: Sums of almost zero-dimensional spaces. Topol. Proc. 29(1), 1–12 (2005)

    MathSciNet  MATH  Google Scholar 

  5. Michael, E.: Topologies on spaces of subsets. Trans. Amer. Math. Soc. 71, 152–182 (1951)

    Article  MathSciNet  Google Scholar 

  6. van Mill, J., Pol, R.: On spaces without non-trivial subcontinua and the dimension of their producs. Topol. Appl. 142, 31–48 (2004)

    Article  Google Scholar 

  7. van Mill, J.; The Infinite-Dimensional Topology of Function Spaces. North-Holland Mathematical Library, 64. North-Holland Publishing Co., Amsterdam, 2001. xii+630 pp. ISBN: 0-444-50557-1

  8. Nadler Sam B. Jr.Dimension theory: an introduction with exercises. Sociedad Matemática Mexicana. México 2002

  9. A. Zaragoza, Symmetric products of Erdős space and complete Erdős space. Topology Appl. 284 (2020), 107355, 10 pp

Download references

Acknowledgements

I would like to thank Professor Roman Pol for his helpful suggestions on the topic of this paper.

Funding

This research was supported by a CONACyT doctoral scholarship with number 696239.

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior s/n, Ciudad Universitaria, Coyoacán, 04510, Mexico City, Mexico

    Alfredo Zaragoza

Authors
  1. Alfredo Zaragoza
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alfredo Zaragoza.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work is part of the doctoral work of the author at UNAM, Mexico city, under the direction of the R. Hernández-Gutiérrez.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zaragoza, A. Hyperspaces of dimension 1. Bol. Soc. Mat. Mex. 28, 48 (2022). https://doi.org/10.1007/s40590-022-00441-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40590-022-00441-8

Keywords

Mathematics Subject Classification

Search

Navigation