# zbMATH — the first resource for mathematics

Generalized homogeneity of curves and a question of H. Kato. (English) Zbl 0767.54030
A space $$X$$ is said to be homogeneous with respect to open maps provided that for each two points $$p$$ and $$q$$ of $$X$$ there is an open map $$f$$ of $$X$$ onto itself such that $$f(p)=q$$. A dendroid is an arcwise connected hereditarily unicoherent metric continuum. It is shown that no dendroid is homogeneous with respect to open maps.
##### MSC:
 54F55 Unicoherence, multicoherence
##### Keywords:
homogeneity; dendroid; open maps