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For questions about tropical geometry, piece-wise linear functions with integer slopes, tropical degenerations and applications of tropical geometry, max-plus algebra, and tropical semifields.

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Can Hausdorff dimension make sets into a Tropical Semiring?

Actually, the inequality for the Hausdorff dimension of product sets goes the other way (fixed in the OP now): $$ \dim_{X\times Y}(U_1\times U_2) \ge \dim_X(U_1)+\dim_Y(U_2). $$ And you probably ne …
Pablo Shmerkin's user avatar