1. Therefore, every nontrivial linearly ordered group is infinite. 2. Consider a countable neighborhood basis at, linearly ordered by reverse inclusion with. 3. For example, a linearly ordered group that is Archimedean is an Archimedean group. 4. The patches of a repository are linearly ordered . 5. Because Cantor implicitly assumed that cardinalities are linearly ordered , this case cannot occur. 6. One can also glue together different linearly ordered sets to form a circularly ordered set. 7. The set of all Dedekind cuts is itself a linearly ordered set ( of sets ). 8. Examples of chainable continua include compact connected linearly ordered spaces and in particular closed intervals of real numbers. 9. A subset which is-as a sub-poset-linearly ordered , is called a chain. 10. Permutations, when considered as arrangements, are sometimes referred to as " linearly ordered " arrangements.
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