Arcwise connected continuum with a free arc and with the fixed set property for monotone onto maps

Abstract

We present an arcwise connected continuum with a free arc and with the fixed set property for (open) monotone onto maps which is not a simple closed curve. This answers a question of Y.

Ohsuda (posed 10/31/83, Problem 181 of the Houston Problem Book) in negative.

Keywords

• continuum
• free arc
• fixed set property
• monotone mapping