User:Leigh.Samphier/Topology/Sober Space need not be T1

This page needs proofreading. Please check it for mathematical errors. If you believe there are none, please remove {{Proofread}} from the code. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Proofread}} from the code.

Theorem

Let $\struct{S, \tau}$ be a sober space.

Then:

$\struct{S, \tau}$ need not be a $T_1$ space

Proof

$\blacksquare$

Also see

• User:Leigh.Samphier/Topology/T1 Space need not be Sober

Sources

• 2012: Jorge Picado and Aleš Pultr: Frames and Locales: Chapter $1$: Spaces and Lattices of Open Sets, $\S 3$ Summing up, Paragraph $3.3$