# zbMATH — the first resource for mathematics

Generalized homogeneity of continua and a question of J. J. Charatonik. (English) Zbl 0635.54017
A continuum X has the property of Kelley provided that for each $$\epsilon >0$$, there is a $$\delta >0$$ such that for each two points a and b in X satisfying $$d(a,b)<\delta$$ and for each subcontinuum A of X containing a, there exists a subcontinuum B of X containing b and such that the Hausdorff distance $$d_ H(A,B)<\epsilon$$. The author constructs a contractible 2-dimensional continuum which is homogeneous with respect to the class of confluent mappings but does not have the property of Kelley. He also constructs a curve with the above properties, answering a question of Charatonik.
Reviewer: J.Grispolakis

##### MSC:
 54F15 Continua and generalizations 54C10 Special maps on topological spaces (open, closed, perfect, etc.)