先に私の見解を書いておくが、ピエロくんの紹介してくれた >>312 PDF が参考になるね（＾＾ The Mathematics of Coordinated Inference: A Study of Generalized Hat Problems (Developments in Mathematics) 2013 edition by Hardin, Christopher S., Taylor, Alan D.
P9 ”In Chapter 7 we start to move further away from the hat problem metaphor and think instead of trying to predict a function's value at a point based on knowing (something about) its values on nearby points. The most natural setting for this is a topological space and if we wanted to only consider continuous colorings, then the limit operator would serve as a unique optimal predictor. But we want to consider arbitrary colorings. Thus we have each point in a topological space representing an agent and if f and g are two colorings, then f ≡a g if f and g agree on some deleted neighborhood of the point a. It turns out that an optimal predictor in this case is wrong only on a set that is "scattered" (a concept with origins going back to Cantor). Moreover, this predictor again turns out to be essentially unique, and this is the main result in Chapter 8.”
