Abstract
If B is an uncountable set then there is a function r : B × B → R + r:B \times B \to {{\mathbf {R}}_ + } for which there is no function t : B → R + t:B \to {{\mathbf {R}}_ + } such that \[ r ( b 1 , b 2 ) ⩽ t ( b 1 ) ⋅ t ( b 2 ) for all b 1 , b 2 ∈ B . r({b_1},{b_2}) \leqslant t({b_1}) \cdot t({b_2})\quad {\text {for all}}\;{b_1},{b_2} \in B. \]
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