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Michalski gave a short and elegant proof of a theorem of A. Kumar whichstates that for each set A in R, there exists a subset B of A which is full inA and such that no distance between points in B is a rational number. He alsoproved a similar theorem for sets in the Euclidean plane. In this paper, wegeneralize these results in some special types of category bases.

A note on sets avoiding rational distances in category bases