### On mappings preserving a family of star bodies.

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We prove that if ${\varrho}_{H}$ and δ are the Hausdorff metric and the radial metric on the space ⁿ of star bodies in ℝ, with 0 in the kernel and with radial function positive and continuous, then a family ⊂ ⁿ that is meager with respect to ${\varrho}_{H}$ need not be meager with respect to δ. Further, we show that both the family of fractal star bodies and its complement are dense in ⁿ with respect to δ.

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