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A continuum-chainable continuum which can not be mapped onto an arcwise connected continuum by a monotone epsilon mapping

Publication at Faculty of Mathematics and Physics |
2013

Abstract

A continuum is called continuum-chainable provided for any pair of points and positive epsilon there exists a finite 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.