Trait Suggestion: Misra's subspace of E_0 S178 is not Extremally disconnected P49

[Moniker1998]

Trait Suggestion

Misra's subspace of E_0 S178 is not Extremally disconnected P49, but this fact is not known to pi-Base today:
link to pi-Base

Proof/References

Let $U = \{a_{\alpha\beta} : \alpha, \beta < \omega_1, \alpha \text{ successor ordinal}\}$. Then $a\in\text{cl}(U)\setminus \text{int}(\text{cl}(U))$ so $\text{cl}(U)$ isn't open.

[yhx-12243]

Do you mean S178?

[Moniker1998]

Yes, sorry.