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