Topological implications in varieties.

In 1997, Coleman showed that a variety V is n-permutable for some n iff every T ₀-topological Algebra in V is T ₁. Here we show that the implication " $T_0\Rightarrow$ sober" is another such characterization for n-permutability. Other implications of a similar nature are given. For example, an n-permutable variety having a majority term satisfies " $T_0\Rightarrow T_2$ ". [ABSTRACT FROM AUTHOR]