chain finite

A poset is said to be chain finite if every chain with both maximal ( and minimal element is finite.

with the standard order relation is chain finite, since any infinite subset of must be unboundedPlanetmathPlanetmath ( above or below. with the standard order relation is not chain finite, since for example {x 0x1} is infinite and has both a maximal element 1 and a minimal element 0.

Chain finiteness is often used to draw conclusionsMathworldPlanetmath about an order from information about its covering relation (or equivalently, from its Hasse diagramMathworldPlanetmath).

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