| 1. | Forgetting the location of the ends results in a cyclic order.
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| 2. | The interval topology forgets the original orientation of the cyclic order.
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| 3. | Dropping the " total " requirement results in a partial cyclic order.
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| 4. | Since there are possible linear orders, there are possible cyclic orders.
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| 5. | A cyclic order obeys a relatively strong 4-point transitivity axiom.
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| 6. | A substantial use of cyclic orders is in the determination of the conjugacy classes of free groups.
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| 7. | To begin with, not every partial cyclic order can be extended to a total cyclic order.
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| 8. | To begin with, not every partial cyclic order can be extended to a total cyclic order.
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| 9. | The cyclic order is addressed by a separation relation which has the properties necessary for appropriate deductions.
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| 10. | Cyclic orders are closely related to the more familiar linear orders, which arrange objects in a line.
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