Develops cube structures on the universal minimal system to study nilsystems, giving alternative proofs for saturation properties and a new algebraic proof that RP^[d] is an equivalence relation even for d=1.
$RP^{[d]}$ is an equivalence relation: An enveloping semigroup proof
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We present a purely enveloping semigroup proof of a theorem of Shao and Ye which asserts that for an abelian group $T$, a minimal flow $(X,T)$ and any integer $d \ge 1$, the regional proximal relation of order $d$ is an equivalence relation.
fields
math.DS 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Cube structures of the universal minimal system, nilsystems and applications
Develops cube structures on the universal minimal system to study nilsystems, giving alternative proofs for saturation properties and a new algebraic proof that RP^[d] is an equivalence relation even for d=1.