Glasnik Matematicki, Vol. 44, No.2 (2009), 479-492.

ON n-FOLD HYPERSPACES OF CONTINUA

Sergio Macias

Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México D. F., C. P. 04510, México
e-mail: macias@servidor.unam.mx

Abstract.   We continue our study of n-fold hyperspaces and n-fold hyperspace suspensions. We present more properties of these hyperspaces.

2000 Mathematics Subject Classification.   54B20.

Key words and phrases.   Absolute retract, cone, continuum, n-fold hyperspace, n-fold hyperspace suspension, n-fold symmetric product, retract, suspension, terminal continuum.

Full text (PDF) (free access)

DOI: 10.3336/gm.44.2.13

References:

  1. J. J. Charatonik, A. Illanes, S. Macias, Induced mappings on the hyperspace Cn(X) of a continuum X, Houston J. Math. 28 (2002), 781-805.
    MathSciNet

  2. D. Curtis and N. T. Nhu, Hyperspaces of finite subsets which are homeomorphic to aleph0-dimensional linear metric spaces, Topology Appl. 19 (1985), 251-260.
    MathSciNet     CrossRef

  3. C. H. Dowker, Mapping theorems for noncompact spaces, Amer. J. Math. 68 (1947), 200-242.
    MathSciNet     CrossRef

  4. J. Dugundji, Topology, Allyn and Bacon, Inc., Boston, 1966.
    MathSciNet

  5. C. Eberhart and S. B. Nadler, Jr., The dimension of certain hyperspaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 19 (1971), 1027-1034.
    MathSciNet

  6. C. Eberhart and S. B. Nadler, Jr., Hyperspaces of cones and fans, Proc. Amer. Math. Soc. 77 (1979), 279-288.
    MathSciNet     CrossRef

  7. R. Escobedo, M. de J. López and S. Macias, On the hyperspace suspension of a continuum, Topology Appl. 138 (2004), 109-124.
    MathSciNet     CrossRef

  8. W. Hurewicz, Sur la dimension des produits cartésiens, Ann. of Math. (2) 36 (1935), 194-197.
    MathSciNet     CrossRef

  9. W. Hurewicz and H. Wallman, Dimension theory, Princeton Univ. Press, Princeton, 1941.
    MathSciNet

  10. A. Illanes, Multicoherence of symmetric products, An. Inst. Mat. Univ. Nac. Autónoma México 25 (1985), 11-24.
    MathSciNet

  11. K. Kuratowski, Topology, Vol. 2, English transl., Academic Press, New York-London; PWN, Warsaw, 1968.
    MathSciNet

  12. M. Levin and Y. Sternfeld, The space of subcontinua of a 2-dimensional continuum is infinitely dimensional, Proc. Amer. Math. Soc. 125 (1997), 2771-2775.
    MathSciNet     CrossRef

  13. S. Macias, On symmetric products of continua, Topology Appl. 92 (1999), 173-182.
    MathSciNet     CrossRef

  14. S. Macias, On the hyperspaces Cn(X) of a continuum X, Topology Appl. 109 (2001), 237-256.
    MathSciNet     CrossRef

  15. S. Macias, On the hyperspaces Cn(X) of a continuum X, II, Topology Proc. 25 (2000), 255-276.
    MathSciNet

  16. S. Macias, On the n-fold hyperspace suspension of continua, Topology Appl. 138 (2004), 125-138.
    MathSciNet     CrossRef

  17. S. Macias, Topics on continua, Pure and Applied Mathematics Series, Vol. 275, Chapman & Hall/CRC, Taylor & Francis Group, Boca Raton, London, New York, Singapore, 2005.
    MathSciNet

  18. S. Macias, On the n-fold hyperspace suspension of continua, II, Glasnik Mat. Ser. III 41(61) (2006), 335-343.
    MathSciNet     CrossRef

  19. S. Macias and S. B. Nadler, Jr., n-fold hyperspaces, cones and products, Topology Proc. 26 (2001/2002), 255-270.
    MathSciNet

  20. S. Macias and S. B. Nadler, Jr., Absolute n-fold hyperspace suspensions, Colloq. Math. 105 (2006), 221-231.
    MathSciNet     CrossRef

  21. S. Macias and S. B. Nadler, Jr., Various types of local connectedness in n-fold hyperspaces, Topology Appl. 54 (2007), 39-53.
    MathSciNet     CrossRef

  22. J. van Mill, Infinite-dimensional topology. Prerequisites and introduction, North-Holland Publishing Co., Amsterdam, 1989.
    MathSciNet

  23. S. B. Nadler, Jr., Hyperspaces of sets. A text with research questions, Monographs and Textbooks in Pure and Applied Mathematics 49, Marcel Dekker, Inc., New York-Basel, 1978.
    MathSciNet

  24. S. B. Nadler, Jr., A fixed point theorem for hyperspace suspensions, Houston J. Math. 5, (1979), 125-132.
    MathSciNet

  25. S. B. Nadler, Jr., Continua whose hyperspace is a product, Fund. Math. 108 (1980), 49-66.
    MathSciNet

  26. S. B. Nadler, Jr., Continuum theory. An introduction, Monographs and Textbooks in Pure and Applied Math. 158, Marcel Dekker, Inc., New York, 1992.
    MathSciNet

  27. S. B. Nadler, Jr., Dimension theory: an introduction with exercises, Aportaciones Matemáticas: Textos #18, Sociedad Matemática Mexicana, México, 2002.
    MathSciNet

  28. J. T. Rogers, Jr., Dimension of hyperspaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 20 (1972), 177-179.
    MathSciNet

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