Abstract:
Trees are partial orders in which every element has a linearly
ordered set of predecessors. Here we initiate the exploration of the
structural theory of trees with the study of different notions of branching
in trees and of condensed trees, which are trees in which every node
is a branching node. We then introduce and investigate two different
constructions of tree condensations – one shrinking, and the other expanding,
the tree to a condensed tree.
