Hypothesis: HR 163:
Every non-well-orderable set has an infinite, Dedekind finite subset.
Conclusion: HR 157:
Theorem of Goodner: A compact \(T_{2}\) space is extremally disconnected (the closure of every open set is open) if and only if each non-empty subset of \(C(X)\) (set of continuous real valued functions on \(X\)) which is pointwise bounded has a supremum.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|
Code: 3
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