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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.
8
votes
Accepted
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 …