A subset B of a tree (T,<T) is a branch if B is a maximal linearly orderedPlanetmathPlanetmath subset of T. That is:

  • <T is a linear ordering of B

  • If tTB then B{t} is not linearly ordered by <T.

This is the same as the intuitive conception of a branch: it is a set of nodes starting at the root and going all the way to the tip (in infinite setsMathworldPlanetmath the conception is more complicated, since there may not be a tip, but the idea is the same). Since branches are maximal there is no way to add an element to a branch and have it remain a branch.

A cofinal branch is a branch which intersects every level of the tree.

Title branch
Canonical name Branch
Date of creation 2013-03-22 12:52:22
Last modified on 2013-03-22 12:52:22
Owner Henry (455)
Last modified by Henry (455)
Numerical id 4
Author Henry (455)
Entry type Definition
Classification msc 05C05
Classification msc 03E05
Related topic TreeSetTheoretic
Related topic ExampleOfTreeSetTheoretic
Defines branch
Defines cofinal branch