✦ LIBER ✦
Maximal chains and cutsets of an ordered set: A menger type approach
✍ Scribed by J. -M. Brochet; M. Pouzet
- Publisher
- Springer Netherlands
- Year
- 1988
- Tongue
- English
- Weight
- 797 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0167-8094
No coin nor oath required. For personal study only.
✦ Synopsis
We prove the following results which are related to Menger's theorem for (infinite) ordered sets. (i) If the space of maximal chains of an ordered set is compact, then the maximum number of pairwise disjoint maximal chains is finite and is equal to the minimum size of a cutset, (i.e. a set which meets all maximal chains). (ii) If the maximal chains pairwise intersect, then the intersection of finitely many is never empty. One corollary of {ii) is that, if the maximal chains pairwise intersect and if one of the maximal chains is complete, then there is an element common to all maximal chains.