Talk:Ziegler spectrum

Are Ziegler spectra sober?
The article currently says in the "Properties" section, that Ziegler spectra often fail to be $$T_0$$, but it being unknown whether they all are sober. But being sober implies being $$T_0$$. So those Ziegler spectra which are not $$T_0$$ can not be sober, answering the open problem. What are thr correct statements? (This was mentioned in the comments of https://mathoverflow.net/questions/320561/does-anyone-use-non-sober-topological-spaces). Columbus240 (talk) 04:50, 19 September 2022 (UTC)