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A definable subset of a Euclidean space X is called perfectly situated if it can be represented in some linear system of coordinates as a finite union of (graphs of) definable 𝓒¹-maps with bounded derivatives. Two subsets of X are called simply separated if they satisfy the Łojasiewicz inequality with exponent 1. We show that every closed definable subset of X of dimension k can be decomposed into a finite family of closed definable subsets each of which is perfectly situated and such that any...
In the paper we deal with a task about two circles touching in a rectangle. The assignment of the task was formulated in a fuzzy way, so solvers understood it differently. We present extracts from the authentic solutions which reflect this phenomenon. We suggest an approach to such tasks, how to solve them and how to assess their solutions.
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