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The space of left orders of a group is either finite or uncountable. (English) Zbl 1215.06009

By introducing a natural topology on the set \(O_G\) of left orderings on a group \(G\), it is shown that \(O_G\) can never be countably infinite.

MSC:

06F15 Ordered groups
20F60 Ordered groups (group-theoretic aspects)
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