Maximal equicontinuous factor and minimal map on finitely suslinean continua

Abstract

In this paper, we introduce the notion of negatively regionally proximal pairs of onto maps which coincides with the set of regionally proximal pair of $f^{-1}$, whenever $f$ is an homeomorphism and we prove the maximal equicontinoues factor for any onto map on a locally connected continuum is monotone. Using this, we prove that if $f$ is a minimal map on a finitely suslinean continua $X$, then $X$ must be a topological circle and $f$ some irrational rotation of circle.