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In mathematics, a dendrite is a certain type of 
topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called po ...
that may be characterized either as a locally connected
In topology and other branches of mathematics, a topological space ''X'' is
locally connected if every point admits a neighbourhood basis consisting entirely of open, connected sets.
Background
Throughout the history of topology, connectedne ...
dendroid or equivalently as a locally connected continuum that contains no simple closed curves.
Importance
Dendrites may be used to model certain types ofJulia set
In the context of complex dynamics, a branch of mathematics, the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function consists of values w ...
. For example, if 0 is pre-periodic, but not periodic, under the function , then the Julia set of is a dendrite: connected, without interior..
References
See also
* Misiurewicz point * Real tree, a related concept defined using metric spaces instead of topological spaces * Dendroid (topology) and unicoherent space, two more general types of tree-like topological space Continuum theory Trees (topology) {{Topology-stub