We have the following indirect implication of form equivalence classes:
| Implication | Reference |
|---|---|
| 135 \(\Rightarrow\) 135 |
Here are the links and statements of the form equivalence classes referenced above:
| Howard-Rubin Number | Statement |
|---|---|
| 135: | If \(X\) is a \(T_2\) space with at least two points and \(X^{Y}\) is hereditarily metacompact then \(Y\) is countable. (A space is metacompact if every open cover has an open point finite refinement. If \(B\) and \(B'\) are covers of a space \(X\), then \(B'\) is a refinement of \(B\) if \((\forall x\in B')(\exists y\in B)(x\subseteq y)\). \(B\) is point finite if \((\forall t\in X)\) there are only finitely many \(x\in B\) such that \(t\in x\).) van Douwen [1980] |
| 135: | If \(X\) is a \(T_2\) space with at least two points and \(X^{Y}\) is hereditarily metacompact then \(Y\) is countable. (A space is metacompact if every open cover has an open point finite refinement. If \(B\) and \(B'\) are covers of a space \(X\), then \(B'\) is a refinement of \(B\) if \((\forall x\in B')(\exists y\in B)(x\subseteq y)\). \(B\) is point finite if \((\forall t\in X)\) there are only finitely many \(x\in B\) such that \(t\in x\).) van Douwen [1980] |
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