Branch (graph theory)

From Wikipedia, the free encyclopedia

 This article or section contains too much jargon and may need simplification or further explanation.
Please discuss this issue on the talk page, and/or remove or explain jargon terms used in the article. Editing help is available.
This article has been tagged since August 2007.

In mathematics, especially mathematical logic and set theory, a branch of a tree T is a map f such that ∀n : f (n) ∈ T.

By a tree on a product set κ1 ×···× κp we mean here a subset of the union of κ1i×···×κpi for all i < ω,

T\subseteq\bigcup_{i<\omega} \kappa_1^i\times\cdots\times\kappa_p^i ~,

closed under initial segments, and the set of branches of such a tree is then more explicitly the set

[T]=\{ (f_1,...,f_p)\mid\forall n\in\omega: (f_1(n),...,f_p(n))\in T\} ~.

This is a closed set for the usual product topology (see AD plus).

[edit] See also


 This mathematical logic-related article is a stub. You can help Wikipedia by expanding it.