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The ANTI-order and the fixed point property for caccc posets

✍ Scribed by Boyu Li; E.C. Milner

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
670 KB
Volume
175
Category
Article
ISSN
0012-365X

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✦ Synopsis

This paper settles a conjecture made in (Li [2]) that, if (PC: ~ ~< 2) is an ANTI-perfect sequence in a connected caccc poset having no one-way infinite fence, then either there are ~ < 2 and x e Pe~+l such that Pc(> x) and P~(<x) are both fixed point free (fpf), in which case P is also fpf, or P has the fixed point property (fpp) if and only if P;, has the fpp.

πŸ“œ SIMILAR VOLUMES

The ANTI-order for caccc posets β€” part I
The ANTI-order for caccc posets β€” part I
✍ Boyu Li πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 860 KB

This paper deals with a generalization of the following simple observation. Suppose there are distinct elements a, b of the chain complete poset (P, <) such that P( < a) C P( < b) and P( > a) L P( > h); if P( < a) and P( > a) are both fixed point free (fpf), then P is also fpf (we say P is trivially

The ANTI-order for caccc posets β€” Part I
The ANTI-order for caccc posets β€” Part II
✍ Boyu Li πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 957 KB

In Part I we defined the ANTI-order, ANTI-good subsets, ANTI-perfect sequences and ANTIcores for caccc posets. In this part we prove the main result: If n = (P. : < < 2.) is an ANTIperfect sequence of a connected caccc poset P which dots not contain a one-way infinite fence, then PC is a retract of

Isotone relations and the fixed point pr
Isotone relations and the fixed point property for posets
✍ James W Walker πŸ“‚ Article πŸ“… 1984 πŸ› Elsevier Science 🌐 English βš– 659 KB

A strengthened form of the fixed point property for posets is presented, in which isotone functions are replaced by more general isotone relations. For finite posets, this 'relational fixed point property' turns out to be equivalent to dismantlability. But an example shows that not every infinite po

A retract characterization of posets wit
A retract characterization of posets with the fixed-point property
✍ Richard A Brualdi; J.A Dias da Silva πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 233 KB

It has been an open problem to characterize posets P with the property that every order-preserving map on P has a fixed point. We give a characterization of such posets in terms of their retracts.