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 mee
The PT-order, minimal cutsets and menger property
โ Scribed by LiBo Yu
- Publisher
- Springer Netherlands
- Year
- 1989
- Tongue
- English
- Weight
- 629 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0167-8094
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
It is shown that, if an ordered set P contains at most k pairwise disjoint maximal chains, where k is finite, then every finite family of maximal chains in P has a cutset of size at most k. As a corollary of this, we obtain the following Menger-type result that, if in addition, P contains k pairwise
Let P be an ordered set. P is said to have the finite cutset property if for every x in P there is a finite set F of elements which are noncomparable to x such that every maximal chain in P meets {x} t.J F. It is well known that this property is equivalent to the space of maximal chains of P being c
## Abstract Let us say that any (Turing) degree **__d__** > **0** __satisfies the minimal complementation property__ (MCP) if for every degree **0** < **__a__** < **__d__** there exists a minimal degree **__b__** < **__d__** such that **__a__** โจ **__b__** = **__d__** (and therefore **__a__** โง **_