Dendroid (topology)
Encyclopedia
In topology
, a hereditarily unicoherent
, arcwise connected continuum
is called a dendroid.
A continuum X is called hereditarily unicoherent if every subcontinuum of X is unicoherent
.
A locally connected dendroid is called a dendrite
.
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, a hereditarily unicoherent
Unicoherent
A topological space X is said to be unicoherent if it is connected and the following property holds:For any closed, connected A, B \subset X with X=A \cup B, the intersection A \cap B is connected....
, arcwise connected continuum
Continuum (topology)
In the mathematical field of point-set topology, a continuum is a nonempty compact connected metric space, or less frequently, a compact connected Hausdorff topological space...
is called a dendroid.
A continuum X is called hereditarily unicoherent if every subcontinuum of X is unicoherent
Unicoherent
A topological space X is said to be unicoherent if it is connected and the following property holds:For any closed, connected A, B \subset X with X=A \cup B, the intersection A \cap B is connected....
.
A locally connected dendroid is called a dendrite
Dendrite (mathematics)
In topology, a locally connected dendroid is called a dendrite. Equivalently a dendrite is a locally connected continuum that contains no simple closed curves....
.