  In this paper, we introduce the notion of $\mathcal{M}$-convergence and
$\mathcal{MN}$-convergence structures in posets, which, in some sense,
generalise the well-known Scott-convergence and order-convergence structures.
As results, we give a necessary and sufficient conditions for each generalised
convergence structures being topological. These results then imply the
following two well-established results: (1) The Scott-convergence structure in
a poset $P$ is topological if and only if $P$ is continuous, and (2) The
order-convergence structure in a poset $P$ is topological if and only if $P$ is
$\mathcal{R}^*$-doubly continuous.
