Abstract
LetG be a compact group andℒ a sublattice of the lattice of all closed subgroups ofG. In Proposition 1 it is shown thatℒ is a complete lattice if it is a closed subset of the spaceG c of all closed non empty subsets ofG. In general the converse of this fact is not true (Example 3), but the following result can be obtained (Theorem 5): Ifℒ is complete and if each element ofℒ is normalized by the connected component of the identity ofG, thenℒ is a closed, totally disconnected subset ofG c. We mention the following corollary: IfG is totally disconnected or abelian, thenℒ is complete if and only if it is a closed subset ofG c.
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