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.

单词	Branch
释义	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.
随便看	DifferenceOfVectors difference of vectors DifferenceQuotient difference quotient DifferenceSet difference set DifferentiableFunction differentiable function DifferentiableFunctionsAreContinuous differentiable functions are continuous Differential differential DifferentialdifferenceEquationsForHypergeometricFunction differential-difference equations for hypergeometric function DifferentialEntropy differential entropy DifferentialEquation differential equation DifferentialEquationOfCircles differential equation of circles DifferentialEquationsForXx differential equations for x^x DifferentialEquationsOfJacobivarthetaFunctions differential equations of Jacobi ϑ functions DifferentialField