13.  Other planar objects

13.1  Dendroids and dendrites

Definition (dendroid). A dendroid (term due to Knaster (1961)) is a locally connected Peano continuum.

Dendroids are a special class of tree-like topological spaces.

Theorem (Borsuk, 1954). Every continuous application of a dendroid in itself has a fixed point.

Definition (dendrite). A dendrite (dendrite) (figure 11 ) is a locally connected dendroid or equivalently a locally connected continuum containing no Jordan curve (i.e. a closed and simple curve) (p. 300 of