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

$<_{T}$ is a linear ordering of $B$

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.
Defines:
branch, cofinal branch
Related:
TreeSetTheoretic, ExampleOfTreeSetTheoretic
Type of Math Object:
Definition
Major Section:
Reference
Mathematics Subject Classification
05C05 no label found03E05 no label found Forums
 Planetary Bugs
 HS/Secondary
 University/Tertiary
 Graduate/Advanced
 Industry/Practice
 Research Topics
 LaTeX help
 Math Comptetitions
 Math History
 Math Humor
 PlanetMath Comments
 PlanetMath System Updates and News
 PlanetMath help
 PlanetMath.ORG
 Strategic Communications Development
 The Math Pub
 Testing messages (ignore)
 Other useful stuff
Recent Activity
Jul 5
new correction: Error in proof of Proposition 2 by alex2907
Jun 24
new question: A good question by Ron Castillo
Jun 23
new question: A trascendental number. by Ron Castillo
Jun 19
new question: Banach lattice valued Bochner integrals by math ias
new correction: Error in proof of Proposition 2 by alex2907
Jun 24
new question: A good question by Ron Castillo
Jun 23
new question: A trascendental number. by Ron Castillo
Jun 19
new question: Banach lattice valued Bochner integrals by math ias