>>114
つづき

２）Generalized Hat Problems との関連
スレ45 https://rio2016.5ch.net/test/read.cgi/math/1508931882/473
(抜粋)
　ピエロくんの紹介
https://pdfs.semanticscholar.org/8514/a9f8b30546ea81739b9409132673276713d3.pdf
The Mathematics of Coordinated Inference: A Study of Generalized Hat Problems (Developments in Mathematics) 2013 edition by Hardin, Christopher S., Taylor, Alan D.

７章”The Topological Setting”とかなっていて
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.”
などとある
さすれば、時枝もそのままじゃ（Topologicalな条件を加えないと）、成り立たないと思う
(引用終り)
以上