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

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.

Keywords

• continuum
• continuum-chainable
• monotone mapping
• arcwise connected