Basically disconnected and Tychonoff implies sequentially discrete

[Moniker1998]

This is a slight modification of theorem 10 which says that extremally disconnected locally Hausdorff space is sequentially discrete.
Note that we can't really change Tychonoff to "locally X" because the "locally" would have to be cozero type of locally for this subspace to still be basically disconnected, which is why that part doesn't generalize.

In particular this theorem implies #1423 is not basically disconnected

[prabau]

Nice result. The contrapositive shows that 7 more spaces are not basically disconnected (many of them well known spaces: $\omega_1$, Sorgenfrey plane, etc)