  For a stochastically monotone Markov chain taking values in a Polish space,
we present a number of conditions for existence and for uniqueness of its
stationary regime, as well as for closeness of its transient trajectories. In
particular, we generalise a basic result by Bhattacharya and Majumdar (2007)
where a certain form of mixing, or swap condition was assumed uniformly over
the state space. We do not rely on continuity properties of transition
probabilities.
