Weak stability conditions and the space of chains of torsion classes

In this paper we show an explicit relation between chains of torsion classes and weak stability conditions over an abelian category. In particular, up to a natural equivalence, they coincide. We investigate topological properties of the space of chains of torsion classes and its quotient given by this equivalence relation. In particular we show that this space is compact if and only if the abelian category has finitely many torsion classes.