Let be the group of all permutations of , viewed as a subspace of Baire space .

How do I prove that there is no left-invariant complete metric on ?

A metric is left-invariant if , for all x, y, z.

Thank you.

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- Jan 16th 2010, 12:21 PMharrietteleft-invariant complete metric on S_\infty
Let be the group of all permutations of , viewed as a subspace of Baire space .

How do I prove that there is no left-invariant complete metric on ?

A metric is left-invariant if , for all x, y, z.

Thank you.