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November 23rd, 2013, 04:30 AM   #1
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Discrete subgroups of isometry group of euclidean space

We say that a subgroup S of G is discrete if and only if subset topology on
S is discrete.

For subgroups of isometry groups of euclidean space an equivalent
condition is: intersection of the S-orbit of any x has finite intersection with any
compact set.

Why is there such the equivalent condition?
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