Meager composants of continua

Abstract

Given a metric continuum X and a point p of X, the meager composant of p in X is defined as the union of all nowhere dense subcontinua of X that contain p. In this paper we study some topological properties of meager composants. In particular, we show that if a continuum contains a meager composant that is not closed, then the continuum must be non-Suslinean. Also, if a hereditarily k-coherent continuum has a non-closed meager composant, then the continuum must contain an indecomposable subcontinuum. Furthermore, if the hypothesis of having a singular dense meager composant is added, then both hereditarily k-coherent continua and irreducible continua must be indecomposable. Additionally, we provide many interesting examples and open problems.