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
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.

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