A topological system is disjoint from every minimal system exactly when it has countably many dense minimal subsets each disjoint from it, with analogous residual-pair and distal characterizations.
Bernshteyn, A short proof of Bernoulli disjointness via the local lemma , Proc
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On systems disjoint from all minimal systems
A topological system is disjoint from every minimal system exactly when it has countably many dense minimal subsets each disjoint from it, with analogous residual-pair and distal characterizations.