Skip to main content
SpringerLink
Log in

On some properties of a certain class of compacta

  • Original Paper
  • Published:
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

Abstract

We introduce the countably measure determined compact spaces, originally due to M. Talagrand, which form a class that is strictly located between the class of compacta carrying a strictly positive Radon probability and the class of those spaces which carry a strictly positive Radon probability of countable (Maharam) type. Some properties of these compact spaces are studied and also some applications are given.

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. Argyros S., Mercourakis S., Negrepontis S.: Functional analytic properties of Corson-compact spaces. Studia Math. 89, 197–229 (1988)

    MathSciNet  MATH  Google Scholar 

  2. Argyros S., Negrepontis S.: On weakly K-countable determined spaces of continuous functions. Proc. Am. Math. Soc. 87, 731–736 (1983)

    MathSciNet  MATH  Google Scholar 

  3. Aron R.M., Boyd C., Ryan R.A., Zalduendo I.: Zeros of polynomials on Banach spaces: the real story. Positivity 7, 285–295 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Banakh T., Plichko A., Zagorodnyuk A.: Zeros of quadratic functionals on nonseparable spaces. Colloq. Math. 100, 141–147 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. Comfort, W.W., Negrepontis, S.: Chain Conditions in Topology, Cambridge Tracts in Mathematics, vol. 79. Cambridge University Press, Cambridge (1982)

  6. Deville, R., Godefroy, G., Zizler, V.: Smoothness and renormings in Banach spaces. Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 64. Longman Scientific and Technical, Harlow (1993)

  7. Ferrer J.: On the zero-set of real polynomials in non-separable Banach spaces. Publ. RIMS 43(3), 685–697 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ferrer J.: Zeroes of real polynomials on C(K) spaces. J. Math. Anal. Appl. 336, 788–796 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ferrer J.: A note on zeroes of real polynomials in C(K) spaces. Proc. Am. Math. Soc. 137(2), 573–577 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ferrer J.: On the controlled separable projection property for some C(K)-spaces. Acta Math. Hung. 124, 145–154 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Godefroy G.: Compacts de Rosenthal. Pacific J. Math. 91, 293–306 (1980)

    MathSciNet  MATH  Google Scholar 

  12. Hrusák M., Szeptycki P.J., Tamariz-Mascarúa A.: Spaces of continuous functions defined on Mrówka spaces. Topol. Appl. 148, 239–252 (2005)

    Article  MATH  Google Scholar 

  13. Plebanek G.: Convex Corson compacta and Radon measures. Fund. Math. 175, 143–154 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Rosenthal H.P.: On injective Banach spaces and the spaces L ∞(μ) for finite measures μ. Acta Math. 124, 205–248 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  15. Rychtár J.: Pointwise uniformly rotund norms. Proc. Am. Math. Soc. 133(8), 2259–2266 (2005)

    Article  MATH  Google Scholar 

  16. Talagrand M.: Separabilité vague dans l’espace des mesures sur un compact. Israel J. Math. 37, 171–180 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  17. Todorcevic S.: Chain-condition methods in Topology. Topol. Appl. 101, 45–82 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wójtowicz M.: Reflexivity and the separable quotient problem for a class of Banach spaces. Bull. Pol. Acad. Sci. Math. 50, 383–394 (2002)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Valencia, Dr. Moliner, 50, 46100, Burjasot (Valencia), Spain

    Jesús Ferrer

Authors
  1. Jesús Ferrer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jesús Ferrer.

Additional information

The author has been partially supported by MEC and FEDER Project MTM2011-22417.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ferrer, J. On some properties of a certain class of compacta. RACSAM 106, 333–339 (2012). https://doi.org/10.1007/s13398-011-0057-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13398-011-0057-z

Keywords

Mathematics Subject Classification (2000)

Search

Navigation