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- Trees (topology)

Hedgehog space

In mathematics, a hedgehog space is a topological space consisting of a set of spines joined at a point. For any cardinal number , the -hedgehog space is formed by taking the disjoint union of real un

Dendrite (mathematics)

In mathematics, a dendrite is a certain type of topological space that may be characterized either as a locally connected dendroid or equivalently as a locally connected continuum that contains no sim

Unicoherent space

In mathematics, a unicoherent space is a topological space that is connected and in which the following property holds: For any closed, connected with , the intersection is connected. For example, any

Real tree

In mathematics, real trees (also called -trees) are a class of metric spaces generalising simplicial trees. They arise naturally in many mathematical contexts, in particular geometric group theory and

Phragmen–Brouwer theorem

In topology, the Phragmén–Brouwer theorem, introduced by Lars Edvard Phragmén and Luitzen Egbertus Jan Brouwer, states that if X is a normal connected locally connected topological space, then the fol

Tree-graded space

A geodesic metric space is called tree-graded space, with respect to a collection of connected proper subsets called pieces, if any two distinct pieces intersect by at most one point, and every non-tr

Dendroid (topology)

In mathematics, a dendroid is a type of topological space, satisfying the properties that it is hereditarily unicoherent (meaning that every subcontinuum of X is unicoherent), arcwise connected, and f

Comb space

In mathematics, particularly topology, a comb space is a particular subspace of that resembles a comb. The comb space has properties that serve as a number of counterexamples. The topologist's sine cu

Infinite broom

In topology, a branch of mathematics, the infinite broom is a subset of the Euclidean plane that is used as an example distinguishing various notions of connectedness. The closed infinite broom is the

Rips machine

In geometric group theory, the Rips machine is a method of studying the action of groups on R-trees. It was introduced in unpublished work of Eliyahu Rips in about 1991. An R-tree is a uniquely arcwis

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