A concrete metric space is constructed whose transfinite and complementary-finite asymptotic dimensions are both omega+1, giving a counterexample to the omega conjecture.
Engelking, Theory of Dimensions: Finite and Infinite
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A metric space with its transfinite asymptotic dimension omega + 1
A concrete metric space is constructed whose transfinite and complementary-finite asymptotic dimensions are both omega+1, giving a counterexample to the omega conjecture.