Glasnik Matematicki, Vol. 48, No. 1 (2013), 167-172.

CONTINUUM-CHAINABLE CONTINUUM WHICH CAN NOT BE MAPPED ONTO AN ARCWISE CONNECTED CONTINUUM BY A MONOTONE EPSILON MAPPING

Pavel Pyrih, Benjamin Vejnar and Luis Miguel García Velázquez

Faculty of Mathematics and Physics, Charles University in Prague, 118 00 Prague, Czech Republic

Faculty of Mathematics and Physics, Charles University in Prague, 118 00 Prague, Czech Republic
e-mail: vejnar@karlin.mff.cuni.cz

Universidad Nacional Autónoma de México, Mexico City, D. F., Mexico
e-mail: lmgarcia@matem.unam.mx


Abstract.   A continuum is called continuum-chainable provided for any pair of points and positive epsilon there exists a finite weak chain of subcontinua of diameter less than epsilon starting at one point and ending in the other. We present an example of a continuum which is continuum-chainable and which can not be mapped onto an arcwise connected continuum by a monotone epsilon mapping. This answers a question posed by W. J. Charatonik.

2010 Mathematics Subject Classification.   54G20, 54F50.

Key words and phrases.   Continuum, continuum-chainable, monotone mapping, arcwise connected.


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DOI: 10.3336/gm.48.1.13


References:

  1. W. J. Charatonik, M. Insall and J. R. Prajs, Connectedness of the representation space for continua, Topology Proc. 40 (2012), 331-336.
    MathSciNet    

  2. S. B. Nadler Jr, Continuum theory. An introduction, Marcel Dekker, New York, 1992.
    MathSciNet    

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