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 closed interval on the real line is unicoherent, but a circle is not.
If a unicoherent space is more strongly hereditarily unicoherent (meaning that every subcontinuum is unicoherent) and
arcwise connected
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties that ...
, then it is called a
dendroid. If in addition it is
locally connected then it is called a
dendrite. The
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
Connected may refer to:
Film and television
* ''Connected'' (2008 film), a Hong Kong ...
states that, for locally connected spaces, unicoherence is equivalent to a separation property of the closed sets of the space.
References
*
External links
*
General topology
Trees (topology)
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