## Hyperspaces of various locally connected subcontinua.(English)Zbl 0979.54012

During the last ten years several interesting subspaces of various hyperspaces were topologically characterized. Examples include the space of all arcs in the plane, the space of all Peano continua in $$\mathbb{R}^3$$, etc. It is usually a difficult task to identify the exact Borel class of an interesting subspace of a hyperspace. In this note the author extends some known results for Euclidean spaces to spaces that contain a copy of the harmonic fan or the harmonic comb, etc.

### MSC:

 54B20 Hyperspaces in general topology 54F15 Continua and generalizations

### Keywords:

harmonic fan; harmonic comb
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