Hypothesis: HR 426:
If \((X,\cal T) \) is a first countable topological space and \((\cal B(x))_{x\in X}\) is a family such that for all \(x \in X\), \(\cal B(x)\) is a local base at \(x\), then there is a family \(( \cal V(x))_{x\in X}\) such that for every \(x \in X\), \(\cal V(x)\) is a countable local base at \(x\) and \(\cal V(x) \subseteq \cal B(x)\).
Conclusion: HR 1:
\(C(\infty,\infty)\): The Axiom of Choice: Every set of non-empty sets has a choice function.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
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Code: 3
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