cofinalの例文

例文

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1. Partially ordered sets without greatest element or maximal elements admit disjoint cofinal subsets.
2. An ordinal is called regular if it is cofinal with any smaller ordinal; otherwise it is singular.
3. For example, the second theorem above fails for the Tychonoff plank if we restrict ourselves to cofinal subnets.
4. For example, the even and odd natural numbers form disjoint cofinal subsets of the set of all natural numbers.
5. Cofinal subsets are very important in the theory of directed sets and cofinal subnet is the appropriate generalization of  subsequence.