Dp-minimality is a common generalization of weak minimality and weak o-minimality. If T is a weakly o-minimal theory then it is dp-minimal (Fact 2.2), but there are dp-minimal densely ordered groups that are not weakly o-minimal. We introduce the even more general notion of inp-minimality and prove that in an inp-minimal densely ordered group, every definable unary function is a union of finitely many continuous locally monotonic functions (Theorem 3.2).
"A monotonicity theorem for dp-minimal densely ordered groups." J. Symbolic Logic 75 (1) 221 - 238, March 2010. https://doi.org/10.2178/jsl/1264433917