An interesting plane dendroid
An invariant of bi-Lipschitz maps
A new numerical invariant for the category of compact metric spaces and Lipschitz maps is introduced. This invariant takes a value less than or equal to 1 for compact metric spaces that are Lipschitz isomorphic to ultrametric ones. Furthermore, a theorem is provided which makes it possible to compute this invariant for a large class of spaces. In particular, by utilizing this invariant, it is shown that neither a fat Cantor set nor the set is Lipschitz isomorphic to an ultrametric space.
Another semigroup characterization of the simple closed curve.
Arc property of Kelley and absolute retracts for hereditarily unicoherent continua
We investigate absolute retracts for hereditarily unicoherent continua, and also the continua that have the arc property of Kelley (i.e., the continua that satisfy both the property of Kelley and the arc approximation property). Among other results we prove that each absolute retract for hereditarily unicoherent continua (for tree-like continua, for λ-dendroids, for dendroids) has the arc property of Kelley.
Arcwise connected and hereditarily smooth continua
Arcwise connected and locally arcwise connected sets
Association and fixed points