The kernels of group homomorphisms are given by this type of subgroup, whose left and right cosets are identical.
A space has this property if and only if any two disjoint closed subsets can be separated by a continuous function by Urysohn's lemma, and those spaces satisfy T4. Extensions that are separable and have this property are Galois. Since A5 has no non-trivial proper subgroups with this property, it is(*) simple. The kernels of group homomorphisms are given by this type of subgroup, whose left and right cosets are identical. For a curve parameterized by arc length, this type of vector is the derivative of the tangent vector with respect to length, and is thus perpendicular to the tangent. For 10 points, independent and identically distributed variables with finite mean and variance will approach this type of distribution according to the central limit theorem.
A space has this property if and only if any two disjoint closed subsets can be separated by a continuous function by Urysohn's lemma, and those spaces satisfy T4.
normal