Vol. 105, No. 2, 1983

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Some topologies on the set of discrete stationary channels

John Cronan Kieffer

Vol. 105 (1983), No. 2, 359–385

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.

Mathematical Subject Classification 2000
Primary: 94A40
Secondary: 54H99
Received: 29 December 1978
Revised: 25 May 1982
Published: 1 April 1983
John Cronan Kieffer