From continua to R-trees
نویسندگان
چکیده
We show how to associate an R-tree to the set of cut points of a continuum. If X is a continuum without cut points we show how to associate an R-tree to the set of cut pairs of X . AMS Classification 54F15,54F05,20F65,20E08
منابع مشابه
Universal maps on trees
A map f : R ! S of continua R and S is called a universal map from R to S if for any map g : R ! S, f(x) = g(x) for some point x 2 R. When R and S are trees, we characterize universal maps by reducing to the case of light minimal universal maps. The characterization uses the notions of combinatorial map and folded subedge of R. MOS Subject Classi cation Primary: 54H25 Secondary: 54F20
متن کاملSemi-terminal Continua in Kelley Spaces
A continuum K in a space X is said to be semi-terminal if at least one out of every two disjoint continua in X intersecting K is contained in K. Based on this concept, new structural results on Kelley continua are obtained. In particular, two decomposition theorems for Kelley continua are presented. One of these theorems is an improved version of the aposyndetic decomposition theorem for Kelley...
متن کاملBeyond The Concept of Manifolds: Principal Trees, Metro Maps, and Elastic Cubic Complexes
Multidimensional data distributions can have complex topologies and variable local dimensions. To approximate complex data, we propose a new type of low-dimensional “principal object”: a principal cubic complex. This complex is a generalization of linear and non-linear principal manifolds and includes them as a particular case. To construct such an object, we combine a method of topological gra...
متن کاملPeriodic Points
B-spaces are a class of uniquely arcwise connected generalized continua, containing trees. In this paper, it is shown that a main result obtained by several authors for existence of periodic points of small periods of mappings of trees is also true for B-spaces.
متن کاملMappings of Trees and the Fixed Point Property
We investigate weakly confluent, universal, and related mappings of trees and their relationships to the fixed point property for tree-like continua. This investigation leads to some new results, to generalizations of some known results, and to a partial solution of a question of H. Cook.
متن کامل