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We define a cardinal function      χ  ( P , Q ) \chi (P,Q)      , where  P  and  Q  are properties of topological spaces. We show that it is consistent and independent that      χ  ( ω  1 , first countable ) = ω  1 \chi ({\omega _1},\;{\text {first}}\;{\text {countable}}) = {\omega _1}      .

The character of 𝜔₁ in first countable spaces