Hypothesis: HR 357:
\(KW(\aleph_0,\aleph_0)\), The Kinna-Wagner Selection Principle for a denumerable family of denumerable sets: For every denumerable set \(M\) of denumerable sets there is a function \(f\) such that for all \(A\in M\), if \(|A| > 1\) then \(\emptyset\neq f(A)\subsetneq A\).
Conclusion: HR 154:
Tychonoff's Compactness Theorem for Countably Many \(T_2\) Spaces: The product of countably many \(T_2\) compact spaces is compact.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N50(E)\) Brunner's Model III | \(E\) is a finite set of prime numbers.For each \(p\in E\) and \(n\in\omega\), let \(A_{p,n}\) be a set of atoms ofcardinality \(p^n\) |
Code: 3
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