Alman
Alman
Yeah, S87 is P6.
I am also reading about Brian's example (S171) (https://mathoverflow.net/a/416752/506958) and noticed that it has not been added yet that it is not regular, since [first countable + T_3 + Lindelöf...
Actually, as ~regular is automatically deduced from that, but it didn't show up in the list, that means that the theorem could be added, instead of just setting regular to...
Already, since scattered implies T_0, T_3 can be relaxed to regular. Regards more weakenings, I am unsure yet. We have examples of spaces that verify 3 of the conditions but...
Check: M. E. Gewand, “The Lindelöf degree of scattered spaces and their products,” Journal of the Australian Mathematical Society (Series A) 37 (1984), 98–105.  In our case, since (X,...
> > In our case, since (X, T) is regular, each point has a closed neighborhoods basis, and as it is first countable, then each point has a countable closed...
> Very nice! I have not read the article yet, but it would be good to have a more direct proof of this Corollary 2.5. Worth asking on mathse. >...
Alright, I will follow the plan at my pace. Thank you for your help and labour. As a noob, it is hard for me to work xD. By experience, your...
Should we ask further in mathse for a more direct proof of the Corollary 2.5?
@prabau @StevenClontz I have read that part of the book again. Let $(X, \tau)$ be a $T_3$ (regular is enough) scattered Lindelöf space with countable pseudocharacter. (Before going on, $X_{\delta}$...