  The ordering of communication channels was first introduced by Shannon. In
this paper, we aim to find a characterization of the Shannon ordering. We show
that $W'$ contains $W$ if and only if $W$ is the skew-composition of $W'$ with
a convex-product channel. This fact is used to derive a characterization of the
Shannon ordering that is similar to the Blackwell-Sherman-Stein theorem. Two
channels are said to be Shannon-equivalent if each one is contained in the
other. We investigate the topologies that can be constructed on the space of
Shannon-equivalent channels. We introduce the strong topology and the BRM
metric on this space. Finally, we study the continuity of a few channel
parameters and operations under the strong topology.
