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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

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