Some topologies are defined
on the set 𝒮 of all discrete stationary channels with given finite input and
output alphabets, which are weaker than the topology of Neuhoff and Shields
arising from the d concept of channel distance. The closure of various subsets
of 𝒮 with respect to certain of these topologies on 𝒮 are determined. For
example, a topology on 𝒮 is introduced with respect to which the set of
weakly continuous channels (the most general class of channels for which
coding theorems of information theory have been obtained) is the closure in
𝒮 of the set of channels with input finite memory and anticipation. As a
by-product, results are obtained on simulating channels by block codes and on
constructing sliding-block codes from block codes using sets called coding
sets.
