Faculty of Mathematics and Physics,
Charles University in Prague,
118 00 Prague,
Universidad Nacional Autónoma de México,
Mexico City, D. F.,
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.