Glasnik Matematicki, Vol. 48, No. 2 (2013), 429-442.

ON STRONGLY FREELY DECOMPOSABLE AND INDUCED MAPS

Javier Camargo and Sergio Macias

Escuela de Matemáticas, Facultad de Ciencias, Universidad Industrial de Santander, Ciudad Universitaria, Carrera 27 Calle 9, Bucaramanga, Santander, A. A. 678, Colombia
e-mail: jcam@matematicas.uis.edu.co

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


Abstract.   Freely decomposable and strongly freely decomposable maps were introduced by G. R. Gordh and C. B. Hughes as a generalization of monotone maps with the property that these maps preserve local connectedness in inverse limits. We prove some relationships between f, Cn(f) and 2f, when f, Cn(f) or 2f belong to the following classes of maps: Almost monotone, quasi-monotone, weakly monotone, freely decomposable or strongly freely decomposable. We correct two corollaries formulated by Jaunusz J. Charatonik in ``On feebly monotone and related classes of maps''. We also present an alternative reformulation of these results.

2010 Mathematics Subject Classification.   54B20, 54E40, 54F15.

Key words and phrases.   Confluent map, continua, freely decomposable map, irreducible continuum, local homeomorphism, monotone map, quasi-monotone map, strongly freely decomposable map.


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DOI: 10.3336/gm.48.2.14


References:

  1. J. Camargo, Some relationships between induced mappings, Topology Appl. 157 (2010), 2038-2047.
    MathSciNet     CrossRef

  2. J. Camargo and S. Macias, On freely decomposable maps, Topology Appl. 159 (2012), 891-899.
    MathSciNet     CrossRef

  3. J. J. Charatonik, Monotone mappings and unicoherence at subcontinua, Topology Appl. 33 (1989), 209-215.
    MathSciNet     CrossRef

  4. J. J. Charatonik, On feebly monotone and related classes of mappings, Topology Appl. 105 (2000), 15-29.
    MathSciNet     CrossRef

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

  6. J. J. Charatonik and P. Pellicer-Covarrubias, On covering mappings on solenoids, Proc. Amer. Math. Soc. 130 (2001), 2145-2154.
    MathSciNet     CrossRef

  7. W. J. Charatonik, Arc approximation property and confluence of induced mappings, Rocky Mountain J. Math. 28 (1998), 107-154.
    MathSciNet     CrossRef

  8. J. B. Fugate and L. Mohler, Quasi-monotone and confluent images of irreducible continua, Colloq. Math. 28 (1973), 221-224.
    MathSciNet    

  9. K. R. Gentry, Some properties of the induced map, Fund. Math. 66 (1969/1970), 55-59.
    MathSciNet    

  10. G. R. Gordh, Jr. and C. B. Hughes, On freely decomposable mappings of continua, Glas. Mat. Ser. III 14(34) (1979), 137-146.
    MathSciNet    

  11. H. Hosokawa, Induced mappings on hyperspaces, Tsukuba J. Math. 21 (1997), 239-250.
    MathSciNet    

  12. A. Illanes and S. B. Nadler, Jr., Hyperspaces. Fundamentals and recent advances, Marcel Dekker, New York, 1999.
    MathSciNet    

  13. K. Kuratowski, Topology. Vol II, Academic Press, New York-London, 1968.
    MathSciNet    

  14. S. Macias, Topics on continua, Chapman & Hall/CRC, London, New York, Singapore, 2005.
    MathSciNet     CrossRef

  15. T. Maćkowiak, Continuous mappings on continua, Dissertationes Math. (Rozprawy Mat.) 158 (1979), 1-95.
    MathSciNet    

  16. S. B. Nadler Jr., Hyperspaces of sets, Unabridged edition of the 1978 original, Sociedad Matemática Mexicana, México, 2006.
    MathSciNet    

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