chain finite
A poset is said to be chain finite if every chain with both maximal (http://planetmath.org/MaximalElement) and minimal element is finite.
with the standard order relation is chain finite,
since any infinite subset of must be
unbounded (http://planetmath.org/UpperBound) above or below.
with the standard order relation is not chain finite,
since for example
is infinite and has both a maximal element and a minimal element .
Chain finiteness is often used to draw conclusions about an order from information about its covering relation (or equivalently, from its Hasse diagram
).
Title | chain finite |
---|---|
Canonical name | ChainFinite |
Date of creation | 2013-03-22 16:55:07 |
Last modified on | 2013-03-22 16:55:07 |
Owner | lars_h (9802) |
Last modified by | lars_h (9802) |
Numerical id | 4 |
Author | lars_h (9802) |
Entry type | Definition |
Classification | msc 06A06 |
Defines | chain finite |