Some Topologies on a set of Information Channels

SYNOPTIC ABSTRACT

In this paper, information channels between a pair of compact Hausdorff spaces with measurable transformations are considered. First, a metric topology is introduced on a set of channels and the completeness property is shown for sets of various types of channels such as stationary, stationary ergodic, AMS and AMS ergodic. Two topologies are then defined on a set of channels using the weak* topology of (probability) measures. Also a convergence property of a sequence of channels is characterized in terms of the output sources or compound sources. Finally, a continuous channel is characterized as the one that preserves weak* convergence of sources.

Key Words and Phrases:

• Channels
• generalized channels
• metric topology
• pointwise weak* topology
• uniform weak* topology
• continuous channels