Rocky Mountain Journal of Mathematics

Hereditarily Unicoherent Continua and Their Absolute Retracts

Janusz J. Charatonik, Wł odzimierz J. Charatonik, and Janusz R. Prajs

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 34, Number 1 (2004), 83-110.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181069893

Digital Object Identifier
doi:10.1216/rmjm/1181069893

Mathematical Reviews number (MathSciNet)
MR2061119

Zentralblatt MATH identifier
1061.54024

Subjects
Primary: 54F15: Continua and generalizations 54F20
Secondary: 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also 55M15] 54E40: Special maps on metric spaces

Keywords
Absolute retract arc approximation property arc component arc property of Kelley confluent continuum decomposable dendroid hereditarily unicoherent property of Kelley retraction tree tree-like unionable

Citation

Charatonik, Janusz J.; Charatonik, Wł odzimierz J.; Prajs, Janusz R. Hereditarily Unicoherent Continua and Their Absolute Retracts. Rocky Mountain J. Math. 34 (2004), no. 1, 83--110. doi:10.1216/rmjm/1181069893. https://projecteuclid.org/euclid.rmjm/1181069893


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References

  • M. Barge and W.T. Ingram, Inverse limits on $[0,1]$ using logistic bonding maps, Topology Appl. 72 (1996), 159-172.
  • R.H. Bing, Snake-like continua, Duke Math. J. 18 (1951), 653-663.
  • K. Borsuk, Theory of retracts, PWN, Warszawa, 1967.
  • J.J. Charatonik, Confluent mappings and unicoherence of continua, Fund. Math. 56 (1964), 213-220.
  • --------, Inverse limits of arcs and of simple closed curves with confluent bonding mappings, Period. Math. Hungar. 16 (1985), 219-236.
  • --------, History of continuum theory, in Handbook of the history of general topology (C.E. Aull and R. Lowen, eds.), Vol. 2, Kluwer Acad. Publ., Dordrecht, 1998, pp. 703-786.
  • J.J. Charatonik and W.J. Charatonik, On projections and limit mappings of inverse systems of compact spaces, Topoology Appl. 16 (1983), 1-9.
  • --------, Montoneity relative to a point and inverse limits of continua, Glas. Mat. Ser. III 20 (40), (1985), 139-151.
  • --------, Fans with the property of Kelley, Topology Appl. 29 (1988), 73-78.
  • J.J. Charatonik, W.J. Charatonik, K. Omiljanowski and J.R. Prajs, Hyperspace retractions for curves, Dissertationes Math. (Rozprawy Mat.) 370 (1997), 1-34.
  • J.J. Charatonik, W.J. Charatonik and J.R. Prajs, Arc property of Kelley and absolute retracts for hereditarily unicoherent continua, Colloq. Math. 97 (2003), 49-65.
  • --------, Kernels in hereditarily unicoherent continua and absolute retracts, Topology Proc. 26 (2001-2002), 127-145.
  • --------, Atriodic absolute retracts for hereditarily unicoherent continua, Houston J. Math., to appear.
  • J.J. Charatonik and J.R. Prajs, On local connectedness of absolute retracts, Pacific J. Math. 201 (2001), 83-88.
  • --------, AANR spaces and absolute retracts for tree-like continua, Czechosl. Math. J., to appear.
  • W.J. Charatonik, Smooth dendroids as inverse limits of dendrites, Fund. Math. 124 (1984), 163-168.
  • --------, Arc approximation property and confluence of induced mappings, Rocky Mountain J. Math. 28 (1998), 107-154.
  • S.T. Czuba, On dendroids with Kelley's property, Proc. Amer. Math. Soc. 102 (1988), 728-731.
  • J. Dugundji, Topology, Allyn and Bacon, Boston, 1966.
  • J. Grispolakis and E.D. Tymchatyn, A universal smooth dendroid, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 26 (1978), 991-998.
  • J.G. Hocking and G.S. Young, Topology, Addison-Wesley, Reading, Mass., 1961.
  • S.T. Hu, Theory of retracts, Wayne State Univ. Press, Detroit, 1965.
  • A. Illanes and S.B. Nadler, Jr., Hyperspaces, M. Dekker, New York, 1999.
  • W.T. Ingram, An atriodic tree-like continuum with positive span, Fund. Math. 77 (1972), 99-107.
  • J. Krasinkiewicz and P. Minc, Nonexistence of universal continua for certain classes of curves, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 24 (1976), 733-741.
  • --------, Approximations of continua from within, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 25 (1977), 283-289.
  • P. Krupski, The property of Kelley in circularly chainable and in chainable continua, Bull. Acad. Polon. Sci. Ser. Sci. Math. 29 (1981), 377-381.
  • --------, Solenoids and inverse limits of sequences of arcs with open bonding maps, Fund. Math. 120 (1984), 41-52.
  • K. Kuratowski, Topology, Vol. 2, Academic Press and PWN, New York, 1968.
  • A. Lelek and D.R. Read, Compositions of confluent mappings and some other classes of functions, Colloq. Math. 29 (1974), 101-112.
  • T. Maćkowiak, Confluent mappings and smoothness of dendroids, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 21 (1973), 719-725.
  • --------, An embedding theorem for tree-like continua, in Colloq. Math. Soc. János Bolyai, vol. 23, Topology, Budapest (Hungary), 1978 (A. Császár, ed.), North-Holland, Amsterdam, 1980, pp. 805-813.
  • --------, Continuous mappings on continua, Dissertationes Math. (Rozprawy Mat.) 158 (1979), 1-95.
  • --------, Retracts of hereditarily unicoherent continua, Bull. Acad. Polon. Sci. Ser. Sci. Math. 28 (1980), 177-183.
  • --------, Extension theorem for a pseudo-arc, Fund. Math. 123 (1984), 71-79.
  • --------, Extension theorems for some classes of continua, Topology Appl. 17 (1984), 257-263.
  • M.C. McCord, Universal $\cal P$-like compacta, Michigan J. Math. 13 (1966), 71-85.
  • J. Mioduszewski, Mappings of inverse limits, Colloq. Math. 10 (1963), 39-44.
  • L. Mohler and J. Nikiel, A universal smooth dendroid answering a question of J. Krasinkiewicz, Houston J. Math. 14 (1988), 535-541.
  • S.B. Nadler, Jr., Hyperspaces of sets, M. Dekker, New York, 1978.
  • --------, Continuum theory, M. Dekker, New York, 1992.
  • J.W. Rogers, Jr., On mapping indecomposable continua onto certain chainable indecomposable continua, Proc. Amer. Math. Soc. 25 (1970), 449-456.
  • R.W. Wardle, On a property of J.L. Kelley, Houston J. Math. 3 (1977), 291-299.
  • G.T. Whyburn, Analytic topology, Amer. Math. Soc., Providence, 1942.