Abstract
Assuming the Singular Cardinals Hypothesis, we prove the following property: σ-CWH: For every singular strong limit cardinal κ and ↗-normal space X such that for some χ < κ , every x ∈ X has a neighborhood base of size ⩽ χ, if every closed discrete subspace of size < κ is σ-separated, then so is every closed discrete subspace of size κ. So for getting a model of the negation of σ-CWH, we require a large cardinal.
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