Hypothesis: HR 163:
Every non-well-orderable set has an infinite, Dedekind finite subset.
Conclusion: HR 78:
Urysohn's Lemma: If \(A\) and \(B\) are disjoint closed sets in a normal space \(S\), then there is a continuous \(f:S\rightarrow [0,1]\) which is 1 everywhere in \(A\) and 0 everywhere in \(B\). Urysohn [1925], pp 290-292.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|
Code: 3
Comments: