branch

A subset $B$ of a tree $(T,<_{T})$ is a branch if $B$ is a maximal linearly ordered subset of $T$ . That is:

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$<_{T}$ is a linear ordering of $B$
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If $t\in T\setminus B$ then $B\cup\{t\}$ 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 sets 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